Connectivity maintenance and coverage preservation in wireless sensor networks

Ad Hoc Networks 3 (2005) 744–761 www.elsevier.com/locate/adhoc

Connectivity maintenance and coverage preservation in wireless sensor networks Di Tian *, Nicolas D. Georganas

*

Distributed and Collaborative Virtual Environments Research Laboratory (DISCOVER), School of Information Technology and Engineering, University of Ottawa, 800 King Edward Avenue, 550 Cumberland, Ottawa, ON, Canada K1N 6N5 Received 1 December 2003; accepted 1 March 2004 Available online 9 April 2004

Abstract In wireless sensor networks, one of the main design challenges is to save severely constrained energy resources and obtain long system lifetime. Low cost of sensors enables us to randomly deploy a large number of sensor nodes. Thus, a potential approach to solve lifetime problem arises. That is to let sensors work alternatively by identifying redundant nodes in high-density networks and assigning them an off-duty operation mode that has lower energy consumption than the normal on-duty mode. In a single wireless sensor network, sensors are performing two operations: sensing and communication. Therefore, there might exist two kinds of redundancy in the network. Most of the previous work addressed only one kind of redundancy: sensing or communication alone. Wang et al. [Intergrated Coverage and Connectivity Configuration in Wireless Sensor Networks, in: Proceedings of the First ACM Conference on Embedded Networked Sensor Systems (SenSys 2003), Los Angeles, November 2003] and Zhang and Hou [Maintaining Sensing Coverage and Connectivity in Large Sensor Networks. Technical report UIUCDCS-R-2003-2351, June 2003] first discussed how to combine consideration of coverage and connectivity maintenance in a single activity scheduling. They provided a sufficient condition for safe scheduling integration in those fully covered networks. However, random node deployment often makes initial sensing holes inside the deployed area inevitable even in an extremely high-density network. Therefore, in this paper, we enhance their work to support general wireless sensor networks by proving another conclusion: ‘‘the communication range is twice of the sensing range’’ is the sufficient condition and the tight lower bound to ensure that complete coverage preservation implies connectivity among active nodes if the original network topology (consisting of all the deployed nodes) is connected. Also, we extend the result to k-degree network connectivity and k-degree coverage preservation.
2004 Elsevier B.V. All rights reserved. Keywords: Coverage; Network connectivity; Scheduling integration; Redundancy; Wireless sensor networks

*

Corresponding authors. Address: 1504-25 Leith Hill Rd., Toronto, Canada M2J 1Z1. Tel./fax: +1 416 4918631. E-mail addresses: [email protected] (D. Tian), [email protected] (N.D. Georganas).

1570-8705/$ - see front matter
2004 Elsevier B.V. All rights reserved. doi:10.1016/j.adhoc.2004.03.001

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1. Introduction Recently, the concept of wireless sensor networks has attracted a great deal of research attention due to a wide-range of potential applications that will be enabled by such networks, such as battlefield surveillance, machine failure diagnosis, biological detection, home security, smart spaces, inventory tracking, etc. [1–4]. A wireless sensor network consists of tiny sensing devices, deployed in a region of interest. Each device has processing and wireless communication capabilities, which enable it to gather information about the environment and to generate and deliver report messages to the remote base station (remote user). The base station aggregates and analyzes the report messages received and decides whether there is an unusual or concerned event occurrence in the monitored area. In wireless sensor networks, the energy source provided for sensors is usually battery power, which has not yet reached the stage for sensors to operate for a long time without recharging. Moreover, since sensors are often intended to work in remote or hostile environments, such as a battlefield or desert, it is undesirable or impossible to recharge or replace the battery power of all the sensors. However, long system lifetime is always expected by many monitoring applications. The system lifetime, which is measured by the time till all nodes have been drained out of their battery power or the network no longer provides an acceptable event detection ratio, directly affects network usefulness. Therefore, conserving energy resource and prolonging system lifetime is an important issue in design of large-scale wireless sensor networks. Due to low cost of sensors, it is well accepted that wireless sensor networks can be deployed with a very high node density (even up to 20 nodes/m3 [5]). In such high-density networks with energy efficient design requirement, it is not desirable to have all nodes continuously monitoring the environment all the time. If all the sensors were vigilant at the same time, a single event would trigger many sensors to generate report messages. When these sensors intend to send their highly redundant report messages simultaneously, the network would suffer excessive energy consumption and packet collision. Recent research advances have shown that energy saving can be achieved by assigning a subset of nodes to provide monitoring service at any instant in a high-density network. In the literature, some algorithms [6–8] have been proposed for dynamically scheduling node activity to minimize the number of active nodes while maintaining the original system sensing coverage and the quality of monitoring service. Monitoring is just one duty assumed by sensors. Due to limited communication capability, each sensor node has to act as router to help others to forward data packets to remote base stations. Similarly, redundancy also exists in communication domain in high-density networks. Excessive amount of energy would be wasted by having all nodes to continuously listen to the media, if adaptively turning off radio of some nodes has no influence on network connectivity and communication performance. In the literature, several protocols [9–11] have been proposed for dynamic management of node activity in communication domain. In high-density wireless sensor networks, energy waste always exists if only one kind of redundancy is identified and removed from the network. Minimizing active nodes has to maintain both network connectivity and sensing coverage. Without sufficient coverage, the network cannot guarantee the quality of monitoring service. Without network connectivity, active nodes may not be able to send data back to remote base stations. Most of the previous work addressed only one kind of redundancy: sensing or communication alone. [13,14] are the earliest papers to address how to combine consideration of coverage and connectivity maintenance in a single activity scheduling. They both proved that ‘‘the communication range is at least twice of the sensing range’’ is the sufficient condition to ensure that a full coverage of a convex area implies connectivity among active nodes inside the convex area. However, we argue that their proofs only guarantee safe integration of scheduling in those networks where all the deployed nodes can cover a convex hull without sensing holes inside. Random sensor deployment (such as throwing sensors from a plane) is always believed to be one of the major advantages of wireless sensor networks over traditional wired sensor networks. In such randomly deployed networks, it is hard or impossible to 100% guarantee complete coverage of the monitored region even if the node density is very high. Therefore, in this paper, we first enhance

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their work in order to support general random wireless sensor networks by providing the proof of another conclusion: ‘‘the communication range is twice of the sensing range’’ is the sufficient condition and the tight lower bound to ensure that complete coverage preservation implies connectivity among active nodes if the original network topology (consisting of all the deployed nodes) is connected. It is worth to notice that node-scheduling algorithms with the capability of complete coverage preservation have existed in the literature [6,7]. Also, we extend the result to figure out the relationship between k-degree network connectivity and k-degree coverage preservation to support different applications that may require different tolerance against node failures. Finally, we verify our analytical results through experiments. The rest of this paper is organized as follows. Section 2 presents a review of the related work in the literature. In Section 3, we provide definition for all the terms and notations used in the next sections. In Section 4, we figure out the relationship between connectivity maintenance and coverage preservation. In Section 5, we extend the result in Section 4 to higher degree. In Section 6, we present some experimental results. In Section 7, we conclude the paper.

2. Literature review Minimizing energy consumption and prolonging the system lifetime is an important issue for wireless ad hoc networks. Controlling network topology and scheduling node activity as a promising approach have been studying actively and broadly recently. There are several ways for topology control in the literature. The first approach tries to reduce energy consumption in overhearing by restricting relay stations to a subset of the nodes in a network graph. [9–12 and etc.] fall into this category. In GAF [9], each node knows its geographic location and uses this information to divide a given area into fixed square grids. The size of grid is designed to ensure that any pair of nodes within adjacent grids can directly communicate with each other. Thus, the algorithm selects only one node in each grid to relay packets at any instant and makes other nodes go into sleep mode to save energy. Unlike GAF, [10,11] decide if a node should serve as a dominating node (relay station) based on connectivity among its neighbors. They differ in how to remove redundant dominating nodes caused by simultaneously marking. In Ascent [12], each node self-determines its participation into multi-hop routing as a relay station, based on its contribution to network connectivity. Different from the above algorithms that are based on position information or neighbor connectivity, each node in Ascent evaluates the contribution by checking its local node density and measured message loss rate. The second approach is to let each node adaptively self-configure its radio status while minimizing the impact on global connectivity and communication performance. For instance, Xu et al. [15] proposed a scheme in which energy is conserved by letting nodes turn off their radio when they are not involved into data communication (transmitting and receiving). They also present how to leverage neighbor size to increase the duration of the sleeping time. The third approach restricts which neighbors can communicate with each concerned node, thereby forming an underlying subnetwork owning a lower node degree than the original one. In this way, transmission power and traffic interference in routing and searching can be reduced. [16–18] presented distributed and localized algorithms to form a minimum-power topology, which contains the minimum-power paths between any pair of nodes. The difference between them is that [16,17] rely on location information, while [18] uses direction information. Unlike them, other algorithms try to take advantage of properties of some well-known graphs. For instance, [19] proposed routing algorithms based on prior constructed Gabriel graph, relative neighborhood graph and Delaunay triangulation. It also presented a localized algorithm to form a planar Delaunay triangulation. All the above topology control techniques are based on a communication network graph. They do not address the issue of sensing redundancy.

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In the recent years, some research efforts have been made on sensing coverage in wireless sensor network. [20] presented how to use ILP (Integer Linear Program) technique to solve several optimal 0/1 node scheduling problems in wireless sensor networks. For example, what is the minimal active node set that can completely cover a sensor field? [21] designed a heuristic approach to find k-sets of nodes so that each node set can cover the whole monitored area and the cardinality of node sets is maximal. The approaches presented in the above two papers are both centralized, therefore requiring collection of global information. [6–8] provided alternative, suboptimal, distributed algorithms to solve same or similar problems. In [8], a subset of sensor nodes is selected out initially and operates in active mode until they run out of their energy or are destroyed. Other nodes fall asleep and wake up occasionally to probe their local neighborhood. If there is no working node within its probing range, a sleeping node starts to work, otherwise it sleeps again. In [8], probing range can be adjusted to control sensing redundancy. However, the original sensing coverage may be reduced after node scheduling. Tian and Georganas [6] proposed a distributed node-scheduling algorithm that can provide complete coverage preservation. In their algorithm, each node arithmetically calculates the union of all the sectors covered by its neighbors and determines its working status according to the calculation result. Yan et al. [7] presented another distributed node-scheduling algorithm, wherein each node divides its sensing area into small grids. For a grid, each sensor node sorts those neighbors that can cover this grid, in the ascending order of their associated reference points. Based on the sequence of the reference points, the nodes in the sequence can coordinate their on-duty time in order to continuously monitor that concerned grid. By merging the results of all the covered grids, each node can finally determine its working time. Their algorithm can support k-degree coverage preservation by extending each nodeÕs workspace proportionally along the sequence of reference points. Like those topology control techniques introduced before, the above algorithms still remove one kind of redundancy without addressing the other (i.e. in communication domain). To the best of our knowledge, [13,14] are the earliest papers discussing how to integrate activity scheduling in both domains: communication and sensing. Both of them independently proved the same conclusion: if a convex region is completely covered by a set of nodes, the communication graph consisting of these nodes is connected when R P 2r. In this paper, we enhance their work by providing the proof: if an original network is connected and the identified active nodes can cover the same region as all the original nodes, then the active nodes are connected when R P 2r. The difference between their conclusion and ours can be better understood through a simple scenario as illustrated in Fig. 1. In this scenario, the sensing field can be divided into four subfields 1–4, with each subfield completely covered by a subset of nodes. We call the node subset as subset 1–4 correspondingly. There are two narrow gaps in the middle of the sensing field that cannot be monitored by any node. Furthermore, the communication graph consisting of all the nodes are connected. After node scheduling, redundant nodes is removed from each subset without changing the coverage graph. According to the work in [13,14], we can only know that the active nodes within each subset are connected with each other, but cannot determine if the active nodes among different subsets are connected. However, the latter can be confirmed to be affirmative, according to the proofs in the next sections. Besides theoretical result, [13,14] proposed a distributed protocol to identify redundant nodes in sensing domain, respectively. Both protocols were designed based on the same theorem: a convex area is completely covered by a set of nodes if all the intersection points inside the area are covered. Moreover, [13] presented how to integrate the proposed protocol with the existing SPAN protocol [11] for R < 2r cases. It is worth to mention that there are some other papers discussing coverage problem for wireless sensor networks. However, the definition of their coverage is different from the one addressed above. In the above papers, coverage is the geographical area that can be covered by at least one sensor node. While in [22–25], coverage is used to indicate with how much confidence, the sensors can detect an intruded object penetrating through the network. [24] presented a centralized method using Vornonoi diagram and Delaunay triangulation to find minimal exposure path (a path connecting two points which maximizes the distance of the path to all sensor nodes) and maximal exposure path (a path connecting two points which maximizes

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1

3

2

4

Fig. 1. Illustration of difference between the proof in [13,14] and that in this paper.

the smallest observability of all the points on the path) in a network graph, respectively. In [23], another centralized approach was designed to find a path connecting two points that minimizes the integral observability along the path. Clouqueur et al. [22] introduced energy and noise into sensing model. Based on their sensing model, they proposed a centralized solution to find a minimum exposure path. Li [25] revisited the maximal exposure path problem and proposed a localized, distributed solution. Also, they extended their algorithm to find a maximal exposure path with least energy consumption and smallest traveling distance. Besides activity scheduling, node deployment strategies are directly related with sensing coverage, as well. [26] addressed how to use ILP (Integer Linear Programming) technique to solve such problems: (i) given a grid-based region and types of a sensor set, determine where to deploy these sensors to minimize the overall sensor cost under a certain coverage constraint (for example, each grid is covered at least by k nodes). (ii) how to deploy sensor nodes to ensure that each grid can be covered by an unique node subset so that target position can be determined by identifying the set of observers. [27] presented a sequential node deployment strategy that, instead of deploying all the nodes at one time, adds the nodes step by step until the desired minimum exposure is achieved. 3. Preliminaries To facilitate the future description, we first define some terms and notations used in the future. We view a wireless sensor network from two perspectives: communication and sensing. 3.1. Communication model We assume that two sensors can directly exchange messages if their Euclidean distance is not larger than a communication range R and the communication range is homogeneous among all the sensors in a network. We characterize a wireless sensor network as a communication graph G(V,E), where each element in the node set V(G) represents a sensor in the network. For any pair of nodes v and u in V(G), the edge (v,u) is in the edge set E(G) if and only if the Euclidean distance between v and u, denoted as d(v,u), is not larger than the communication range R. We call two nodes are adjacent if they are incident to a common edge. The neighbor set of node v, denoted as N(v), is the set of those nodes that are adjacent to node v. In other words, N(v) contains all the other nodes that are located within the communication range R away from node v. Each node in N(v) is called a neighbor of node v. We define a path P in G(V,E) as an alter-

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nating sequence of nodes in V(G) and edges in E(G), with each edge being incident to the nodes immediately proceeding and succeeding it in the sequence. P can be represented by its complete edge sequence as P P = (n1, n2)(n2, n3)


(nl2, nl1)(nl1,nl) or simplified as n1 $ nl . We call two nodes v and u in V(G) connected if there is a path P in G(V,E), whose ends are the given nodes, and the whole graph G(V,E) connected if every pair of nodes in V(G) is connected. 3.2. Sensing model Next, we introduce the concept of sensing coverage into a network graph G(V,E). We define A as the region where sensors are initially deployed in and are supposed to monitor afterwards. We assume each sensor can do 360 observation. We denote the maximal circular area centered at a sensor that can be covered by that sensor as its sensing area S(v). The radius of S(v) is called sensor vÕs sensing range. We assume that all sensors have the same sensing range r. We also define the coverage C(X) of a node set X, as the union of sensing area covered by each node in X i.e. C(X) = ["v2XS(v). The overall sensing coverage of a network graph G(V,E) is C(V(G)) = ["v2V(G)S(v). 3.3. Sensing scheduling with coverage preservation We do not restrict our discussion on those networks whose initial sensing coverage is always the same or larger than the expected monitoring region A. Instead, we consider general networks that may have small ‘‘sensing holes’’ geographically scattered throughout the deployed area. We argue that the latter is more realistic situation because wireless sensor networks use a random node deployment strategy. Such a strategy implies that it is difficult or impossible to completely ensure that each point in the region A can be covered by at least one sensor node even at a very high node density. However, it is possible that after removing some sensing redundant nodes, the remaining nodes can cover the same area as initially, without introducing any coverage loss. There have been such node-scheduling algorithms in Refs. [6,7]. Such algorithms assign each sensor node a sensing status, active or inactive. Accordingly, the node set V(G) in the initial network graph G(V,E) is divided into two parts: Vactive(G) and Vinactive(G). Vactive(G) consists of all the nodes obtaining an active status after scheduling. Vinactive(G) contains the others, i.e. Vinactive(G) = V(G)  Vactive(G). We are interested in a subgraph of G(V,E), denoted as G(Vactive), which is induced by the node set Vactive(G), with the edge set as the subset of E(G) consisting of those edges whose both ends are in Vactive(G). We also define an active path as a path in G(V,E), whose all the immediate nodes are active ones. The counterpart is inactive path owning at least one inactive immediate node. If nodes u and v in V(G) can be communicated through an active active path, we call these two nodes are actively connected, denoted as u $ v. 4. Network connectivity on coverage preservation As mentioned above, some existing node-scheduling algorithms have the capability of complete coverage preservation, i.e. C(Vactive) = C(V). Next, we will prove that R P 2r is the sufficient condition and the tight lower bound to ensure connectivity of any subgraph G(Vactive) induced from a connected network graph G(V,E), here the induced subgraph G(Vactive) satisfied that the condition: C(Vactive) = C(V). Our proof is based on the following assumptions: 1. There may be a large number of sensor nodes in the network. However, the number is always finite. 2. There are no two nodes located at the exactly same position. First, we prove the sufficient condition.

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Lemma 1. If R P 2r and C(Vactive) = C(V), let node u and node v be any pair of nodes in V(G) satisfying (i) u 2 Vinactive(G), (ii) 2r < d(u,v) 6 R, then there must exist another node w satisfying (i) w 2 Vactive(G), (ii) w 2 N(v), (iii) w 2 N(u), (iv) d(u,w) 6 2r. Proof. As illustrated in Fig. 2, suppose segment uv interacts with the boundary of S(u) at the point P, there must exist an active node, assumed w, whose distance to point P is not larger than sensing range r. Otherwise, the system overall sensing coverage would be reduced after node scheduling (because point P can be covered by the inactive node u, but cannot be reached by any active node). The position of node w is determined by its distance to point P and the angle a with 0 6 d(w,P) 6 r and 0 6 a 6 p. According to trigonometry, qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi dðv; wÞ ¼ dðw; P Þ2 þ dðv; P Þ2  2  dðw; P Þ  dðv; P Þ  cos a; here d(v,P) = d(u,v)  r. The above expression gets its maximal value d(u,v) when and only when d(w,P) = r and a = p. In other words, when and only when node w is located at the same place as node u. Since there are no two nodes in the network located at the same position, d(v,w) must be smaller than d(u,v). Because d(u,v) 6 R, we have d(v,w) 6 R. Furthermore, 2

2

dðu; wÞ ¼ dðu; P Þ þ dðw; P Þ  2  dðu; P Þ  dðw; P Þ  cosðp  aÞ; where d(u,P) = r . d(u,w) gets its maximal value 2r when and only when d(w,P) = r and a = 0, i.e. node w is located at point Q. { R P 2r, ) node w is adjacent to node u. Therefore, we conclude that for any neighboring node located farther than twice of the sensing range away from an inactive node, there must exist another active node in the network that is adjacent to both them and is located within twice of the sensing range from the inactive node, if the communicate range is larger than twice of the sensing range and the overall sensing coverage is completely preserved after node scheduling. h Lemma 2. If C(Vactive) = C(V), let node u and node v be any pair of nodes in V(G) satisfying (i) u 2 Vinactive(G), (ii) d(u,v) 6 2r, then there must exist another node w satisfying (i) w 2 Vactive(G), (ii) Q 2 S(w), where point Q is the intersection point between segment uv and the boundary of S(v) as illustrated in Fig. 3. Proof. We split out consideration into two cases. Case i: The first case is that node v is an inactive node. Because coverage is completely preserved after node scheduling, there must be an active node that can cover point Q. Case ii: We prove the lemma for the case that node v is an active node. Since in the network, there are no two nodes whose positions are exactly the same, there must be other nodes besides node v in the active node

w

α u

P

Q

Fig. 2. Illustration for Lemma 1.

v

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x

751

x w

w P

P

O β u

β

v

Q

u

Q

v

O

R

Fig. 3. Illustration for Lemma 2.

set Vactive(G). Otherwise, the sensing area of node u cannot be completely preserved after node scheduling. Suppose in Vactive  {v}, node w has the minimal distance to point Q. Assume d(w,Q) = r + g, g > 0. As illustrated in Fig. 3, the segment wQ interacts with the boundary of S(w) at point P. The distance between node w and point P is d(w,P) = r and the distance between point P and point Q is d(P,Q) = d(w,Q)  d(w,P) = g. We consider the following two sub-cases. For the sub-case shown on the left of Fig. 3, i.e. 90 6 angle \PQv 6 180, we can always find a point O, located in segment PQ and satisfying (i) 0 < d(O,Q) = e < g, (ii) 0 < d(O,P) = g  e < g, (iii) O 2 S(u). { d(w,O) = r + g  e > r, ) node w cannot cover point O, qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 2 2 2 2 * dðv; OÞ ¼ dðv; QÞ þ dðO; QÞ  2  dðv; QÞ  dðO; QÞ  cos \PQv P dðv; QÞ þ dðO; QÞ > dðv; QÞ ¼ r; where 90 6 \PQv 6 180 ) node v cannot cover point O, either. If Vactive  {v,w} is not empty, let node x be any node in it, whose distance to point Q is d(x,Q) = r + g + d, d P 0 because w is the node in Vactive  {v} whose distance to point Q is minimal. qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi dðx; OÞ ¼ dðx; QÞ2 þ dðO; QÞ2  2  dðx; QÞ  dðO; QÞ  cos b P dðx; QÞ  dðO; QÞ ¼ r þ g þ d  e P r þ g  e ¼ dðw; OÞ; where 0 6 b 6 p. This implies that if node w cannot cover point O, other active nodes in Vactive  {v,w} cannot, either. Obviously, it contradicts with the condition C(Vactive) = C(V). For the sub-case shown on the right of Fig. 3, i.e. 0 6 angle\PQv < 90, we always find a point O that is located in line PQ, satisfying (i) 0 < d(O,Q) = e 0 < g, (ii) 0 < d(O,P) = g + e 0 > g, (iii) O 2 S(u). { d(w,O) = d(w,Q) + d(Q,O) = r + g + e 0 > r, ) node w cannot cover point O. qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 2 2 2 2 * dðv; OÞ ¼ dðv; QÞ þ dðO; QÞ  2  dðv; QÞ  dðO; QÞ  cos \OQv > dðv; QÞ þ dðO; QÞ > dðv; QÞ ¼ r; where 90 < \OQv = (180  \PQv) 6 180.

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) node v cannot cover point O, either. If Vactive  {v,w} is not empty, let node x be any node in it, whose distance to point Q is d(x,Q) = r + g + d 0 , d P 0. qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi dðx; OÞ ¼ dðx; QÞ2 þ dðO; QÞ2  2  dðx; QÞ  dðO; QÞ  cos b P dðx; QÞ  dðO; QÞ ¼ r þ g þ d0  e0 P r þ g0  e0 > r; where 0 6 b 6 p. This implies that there is no active node that can cover point O. So it contradicts with the condition C(Vactive) = C(V), as well. Therefore, we conclude Lemma 2 by contradiction. Lemma 3. If R P 2r and C(Vactive) = C(V), let node u and node v be any pair of nodes in V(G) satisfying (i) u 2 Vinactive(G), (ii) r < d(u,v) 6 2r, then there must exist another node w satisfying (i) w 2 Vactive(G), (ii) w 2 N(v), (iii) w 2 N(u), (iv) d(u,w) < d(u,v). Proof. As illustrated in Fig. 4, segment uv interacts with the boundary of S(u) at point P. According to Lemma 2, there must exist another node, supposing node w, which is an active one and whose distance to point P does not exceed the sensing range, i.e. 0 6 d(w,P) 6 r. Let the angle of \wPv be b, we have 0 6 b 6 p. According to trigonometry, 2

2

2

dðv; wÞ ¼ dðv; pÞ þ dðw; P Þ  2  dðv; pÞ  dðw; P Þ  cos b; where d(v,P) = r. Obviously, d(v,w) gets its maximal value 2r when and only when d(w,P) = r and b = p, i.e. w is located at point Q. { R P 2r, ) node w is adjacent to node v. Furthermore, 2

2

2

dðu; wÞ ¼ dðu; pÞ þ dðw; P Þ  2  dðu; pÞ  dðw; P Þ  cosðp  bÞ; with d(u,w) reaching its maximal value r + d(u,P) when and only when d(w,P) = r and b = 0, i.e. node w is located at the same place as node v. Since there are no two nodes in the network located at the same position, d(u,w) must be smaller than d(u,v). Also, { v 2 N(u) ) w 2 N(u). Therefore, we conclude that for any neighbor node located within twice of the sensing range and farther than the sensing range away from an inactive node, there must exist another active node in the network that is adjacent to both them and whose distance to that inactive node is smaller than the neighbor node, when the communicate range is at least twice of the sensing range and coverage is completely preserved after node scheduling. h Lemma 4. If R P 2r, let node u, node v and node w be any three nodes in V(G) satisfying (i) 0 < d(u,v) 6 r, (ii) 0 < d(u,w) 6 r, then node v and node w are adjacent to each other. w

β

Q

u

P

v

Fig. 4. Illustration for Lemma 3.

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Proof. As illustrated in Fig. 5, the distance between node v and node w can be expressed as qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi dðv; wÞ ¼ dðu; vÞ2 þ dðu; wÞ2  2  dðu; vÞ  dðu; wÞ  cos /; where 0 < d(u,v) 6 r, 0 < d(u,w) 6 r and 0 6 / 6 p. So d(v,w) gets its maximal value 2r when and only when / = p and d(u,v) = d(u,w) = r. Since R P 2r, we conclude that any pair of nodes, which are located within the sensing range away from a same node, can communicate with each other directly. h Lemma 5. If R P 2r and C(Vactive) = C(V), let node u, node v and node w be any three nodes in V(G) satisfying (i) u 2 Vinactive(G), (ii) v 2 N(u), (iii) w 2 N(u), then node v and node w can communicate with each other directly or through an active path in G(V,E). Proof. According to the distance of node v and node w to node u, we split our consideration into several cases. Case i: 0 < d(u,v) 6 r and R), according to Lemma 3, there must exist another active node x in Vactive(G) satisfying (i) x 2 (N(u)\N(w)), (ii) d(u,x) < d(u,w). It is easy to know v 5 x because x 2 N(w) and v 62 N(w). If we can find node x further satisfying 0 < d(u,x) 6 r, then referring to the conclusion for case i, node v and x are adjacent with each other. Thus, node v and w can communicate with each other via the active path (v,x)(x,w). Otherwise (i.e. r < d(u,x) < d(u,w) 6 2r), according to Lemma 3, there must exist another active node y with (y 5 x 5 w) satisfying that y 2 (N(x)\N(u)) and d(u,y) < d(u,x). If the selected node y is node v, then node v and node w can communicate with each other via the active path (v = y,x)(x,w). Otherwise (i.e. v 5 y 5 x 5 w), if we can find such an active node y further satisfying 0 < d(u,y) 6 r, according to the conclusion for case i, node v and node y are adjacent with each other. Thus, node v and node w can communicate with each other via the active path (v,y)(y,x)(x,w). However, if r < d(u,y) < d(u,x) < d(u,w) 6 2r, there must be another active node z satisfying that z 2 (N(u)\N(y)) and d(u,z) < d(u,y). Similarly, it can be concluded that there is an active path (v = z,y)(y,x)(x,w) or (v,z)(z,y)(y,x)(x,w) unless r < d(u,z) 6 2r. The proof is going on if the new identified active node has a distance to node u larger than the sensing range. Since, the number of nodes in the graph G(V,E) is finite, the process can always end at an active node that equals to node v or whose distance to node u is equal to or smaller than the sensing range.

P

v

φ u w

Q Fig. 5. Illustrate for Lemma 4.

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In any case, there exists a network path between node v and node w whose immediate nodes are all active ones. So we can conclude the Lemma 5 for case ii. Case iii: In {v,w}, one node has a distance to node u equal to or smaller than the sensing range. The other has a distance to node u exceeding twice of the sensing range. Without loss of generality, we assume 0 < d(u,v) 6 r and 2r < d(u,w). If d(v,w) 6 R, then node v and node w can communicate with each other directly. Otherwise (i.e. d(v,w) > R), according to Lemma 1, there must exist another active node x in Vactive(G) satisfying that x 2 (N(u)\N(w)) and d(u,x) 6 2r. According to the conclusions for cases i and ii, node v and node x are active adjacent to each other or can communicate through an active path v $ x. Correspondingly, the active active path between node v and node w is (v,x)(x,w) or v $ x þ ðx; wÞ. Therefore, we conclude the Lemma 5 for case iii. Case iv: Both nodes v and w have a distance to node u larger than the sensing range and equal to or smaller than twice of the sensing range, i.e. r < d(u,v) 6 2r and r < d(u,w) 6 2r. If d(v,w) 6 R, then node v and node w can communicate with each other directly. Otherwise (i.e. d(v,w) > R), similar to the proof process for case ii, we can always get a sequence of active nodes, denoted as x1, x2,. . .,xi, i P 1, satisfying (i) d(u,xi) < d(u,xi  1) <


< d(u,x2) < d(u,x1) < d(u,w), (ii) xj 2 N(u), 1 6 j 6 i, (iii) x1 2 N(w), (iv) xj 2 N(xj  1), 2 6 j 6 i, (v) {r < d(u,xj) P 2r and xj 5 v, 1 6 j < i}, (vi) {0 < d(u,xi) 6 r or xi = v}. If xi = v, we have got an active path between node v and node w as (w, x1)(x1, x2


(xi1, xi = v). Otherwise (i.e. xi 5 v and 0 < d(u,xi) 6 r), since 0 < d(u,xi) 6 r and r < d(u,v) 6 2r, according to the conclusion for case ii, we know that node v and node xi must be adjacent to each other or active connected through an active path v $ xi . Because we have got an active path between node w and node xi as (w, x1)(x1, x2)


(xi1, xi), after concatenating the above two paths, we get an active path between node v active and node w as (w, x1)(x1, x2)


(xi1, xi)(xi, v) or v $ xi þ ðxi ; xi1 Þ


ðx2 ; x1 Þðx1 ; wÞ. Therefore, we conclude the Lemma 5 for case iv. Case v: In {v,w}, one node has the distance to node u larger than the sensing range and equal to or smaller than twice of the sensing range. The other has the distance exceeding twice of the sensing range. Without loss of generality, we assume r < d(u,v) 6 2r and 2r < d(u,w). If d(v,w) 6 R, then node v and node w can communicate with each other directly. Otherwise (i.e. d(v,w) > R), according to Lemma 1, there must exist another active node x in Vactive(G) satisfying that x 2 (N(u)\N(w)) and d(u,x) 6 2r. According to the conclusion for case iv, node v and node x are adjacent to active each other or can communicate through an active path v $ x. So, we can get an active path between node active v and node w as (v,x)(x,w) or v $ x þ ðx; wÞ. Therefore, we conclude the Lemma 5 for case v. Case vi: Both nodes v and w have the distance to node u larger than twice of the sensing range, i.e. 2r < d(u,v) and 2r < d(u,w). If d(v,w) 6 R, then node v and node w can communicate with each other directly. Otherwise (i.e. d(v,w) > R), according to Lemma 1, there must exist another active node x satisfying that x 2 (N(u)\N(w)) and d(u,x) 6 2r. According to the conclusions for case v and case iii, node v and node x are adjacent to each active other or can communicate through an active path v $ x. Thus, we can get an active path between node v active and node w as (v,x)(x,w) or v $ x þ ðx; wÞ. Therefore, we conclude the Lemma 5 for case vi. h Lemma 6. If R P 2r and C(Vactive) = C(V), for any inactive path in G(V,E), there is a corresponding active path in G(V,E), which ends at the same pair of nodes. Proof. Let P0 be an inactive path ending at node u and node v: P0 = (u = w1, w2)(w2, w3)


(wi2, wi1)(wi1, wi = v). In {wj, 2 6 j 6 i  1}, the number of inactive nodes is l with l P 1. Suppose wk is the first inactive immediate node in path P0. We have all wj, 2 6 j 6 k  1 are active ones and the number of inactive nodes in {wj, k + 1 6 j 6 i} is l  1. According to Lemma 5, node wk1 and node wk+1 are adjaactive cent to each other or can communicate through an active path wk1 ! wkþ1 . Thus, we get a new path

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755

P 1 ¼ ðu ¼ w1 ; w2 Þðw2 ; w3 Þ


ðwk2; wk1 Þðwk1; wkþ1 Þðwkþ1; wkþ2 Þ


ðwi1 ; wi ¼ vÞ or active

P 1 ¼ ðu ¼ w1 ; w2 Þ


ðwk2 ; wk1 Þ þ wk1 $ wkþ1 þ ðwkþ1 ; wkþ2 Þ


ðwi1 ; wi ¼ vÞ: In either case, the number of inactive immediate nodes in the new path P1 is one less than that in path P0. In the same way, we can find another new path P2 whose inactive immediate node number is l  2. The process is going on. In each step, the number of inactive immediate nodes is decremented by one. Since the node number in the graph G(V,E) is finite, the number of node in the old path P0 is finite as well. This implies that we can finally get a path between node u and node v in G(V,E), where all immediate nodes are active ones. h Theorem 1. When R P 2r and the system sensing coverage is completely preserved after node scheduling, if a network graph G(V,E) is originally connected, then the induced subgraph G(Vactive) must be connected. Proof. Let node u and node v be any pair of nodes in Vactive(G). { V(G)  Vactive(G) and the network graph G(V,E) is connected, there must exist a path between these two nodes in G(V,E). Let path P be such a path. If P is active, according to the definition of G(Vactive), path P is in G(Vactive). If path P is inactive, according to Lemma 6, we can always find a corresponding path Q between node u and node v in G(V,E), whose all immediate nodes as active ones, i.e. path Q is in G(Vactive). That is, for any pair of nodes in Vactive(G) we can always find a path in G(Vactive) when the original network graph G(V,E) is connected. The proof ends. h Theorem 1 just tells us that R P 2r guarantees connectivity maintenance after complete coverage preservation. It does not imply disconnectivity among active nodes for networks with R < 2r. Consider the simple scenario illustrated in Fig. 6 with R = 1.8r. Node u is the only node assigned an p inactive status after ffiffiffi node scheduling. The distance between any pair of node v, node w and node x is 3r < R. Therefore, the subgraph consisting of the three inactive nodes is still connected. So R P 2r is not the necessary condition to ensure that coverage preservation implies connectivity maintenance. However, we can prove that R = 2r is the tight lower bound for this conclusion. Theorem 2. When R < 2r and the system sensing coverage is completely preserved after node scheduling, the induced network subgraph G(Vactive) may be disconnected even when the original network graph G(V,E) is connected.

v

w u

x

Fig. 6. Connectivity maintenance for R < 2r.

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O

u v

P

Q

w

Fig. 7. Illustration for Theorem 2.

Proof. Assume R = 2r  n, 0 < n < 2r. Let us consider the scenario shown in Fig. 7, node u and node v are adjacent to each other and has a distance between them as 0 < l = d(u,v) < min(r,n,R). Besides node u and node v, there are a sufficient number of nodes located on the circle centered at node u with a radius as R + e, as illustrated in Fig. 7. e satisfies that 0 < e < l. The union of the sensing areas of these nodes forms a ‘‘ring’’, whose inner radius is R + e  r and whose outer radius is R + e + r. From the figure, we can see that node u can cover part of node vÕs sensing area. The remaining part is a ‘‘crescent’’ that is contained in the ‘‘ring’’. That is because (i) the closed distance from node u to any point in the ‘‘crescent’’ is r that satisfies r > R + e  r ({ r = 2r  r = R + n  r > R + l  r > R + e  r), and (ii) the farthest distance from node u to any point in the crescent, is d(u,Q) = r + l that satisfies r + l < r + R + e ({ r + l = r + R + l  R < r + R + 0 < r + R + e). This implies that node v can take an inactive status during node scheduling. Before node scheduling, the network is connected because d(u,v) = l < R and d(v,w) = R + e  l < R. However, after removing node v, node u becomes an ‘‘isolated’’ node because its distance to any other active node is R + e > R. Therefore, the proof ends. h Combining the proofs for Theorems 1 and 2, we can conclude that: Theorem 3. R P 2r is the sufficient condition and tight lower bound to ensure that complete sensing coverage preservation implies network connectivity among active nodes in an original connected network graph. The significance of the above conclusions is that it establishes the relationship between connectivity maintenance and coverage preservation, enables us to focus on sensing domain when connectivity and coverage are both required, therefore greatly simplifies the safe integration of activity scheduling in both domains.

5. k-degree connectivity on k-degree coverage preservation The result in previous section can be extended to the relationship between k-degree connectivity and k-degree coverage preservation with k > 1. That is, R P 2r is the sufficient condition to ensure that k-degree coverage preservation implies k-degree connectivity maintenance. Before proving it, we first formulate definitions of k-degree connectivity and k-degree coverage preservation. We call a graph G(V,E) is k-connected if for every subset X of V(G) with fewer than k elements,

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757

C(Y) C(X) P C(Vinactive )

Fig. 8. Illustration of Theorem 4.

V(G)  X is connected. We call a node-scheduling algorithm can preserve k-degree coverage if for every inactive node identified by that algorithm, any point in its sensing area can be covered by at least k active nodes. Similar to 1-degree coverage preservation explained in the previous section, this definition accepts the situation that part of expected monitoring area A is weakly covered initially due to random node deployment, i.e. the following discussion is not restricted to those networks where every point in the expected monitoring area A must be covered by at least k nodes before node scheduling. It just requires that node-scheduling algorithms can guarantee that the initially weak coverage would not be exacerbated. Theorem 4. When R P 2r and the system sensing coverage is completely k-degree preserved after node scheduling, if a network graph G(V,E) is originally k-connected, then the induced subgraph G(Vactive) must be k-connected. Proof. Let node set X be any subset of Vactive fewer than k elements. We denote the node subset Vactive  X as Y, consisting of all the other elements in Vactive. Based on coverage definition, C(X)[C(Y) = C(Vactive). Since the original system coverage is preserved after node scheduling, we have C(V) = C(Vactive). * CðV Þ ¼ CðV active þ V inactive Þ ¼ CðV active Þ [ CðV inactive Þ ¼ CðV active Þ; * CðV active Þ  CðV inactive Þ: We can prove that C(Vinactive)  C(Y) by contradiction. Suppose there is a point P in C(Vinactive) satisfying that P 62 C(Y), as shown in Fig. 8. Point P must be in C(X) because C(X)[C(Y) = C(Vactive)  C(Vinactive). According to the definition of k-degree coverage preservation, point P must be covered by at least k active nodes. Since node set X has fewer than k elements, there must be a node in Y, covering point P. It is contradictory with the assumption P 62 C(Y). Therefore, we have C(Vinactive)  C(Y). We can further get C(Y + Vinactive) = C(Y). Based on the definition of k connectivity, the subgraph G(Y + Vinactive) is connected. Also, after removing the node subset Vinactive from the network graph G(Y + Vinactive), the system coverage is not reduced. Therefore, according to Theorem 1, the subgraph G(Y) is also connected. Removing any subset X with fewer than k elements from G(Vactive), the subgraph G(Vactive  X) is still connected. The means G(Vactive) is k-connected. Therefore, the proof ends. h

6. Experimental results The experiments are performed based on the light-weighed sensing simulator implemented for the algorithm in [6]. However, a small modification is made to increase the size of active node set by dividing each nodeÕs sensing area into small grids and determining each nodeÕs status by checking if each grids inside its

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sensing area is covered by a node succeeding the concerned node in the scheduling sequence. It is justified in this context because we concern the connectivity maintenance among minimal active nodes in original connected network graphs instead of simplicity and efficiency of scheduling algorithm. Fig. 9 illustrates

Fig. 9. (a) Overall sensing coverage of a network with 350 nodes in a 100 · 100 m2 region, (b) scheduling result with r as 6 m (black circles representing inactive nodes), (c) network is connected before node scheduling with R = 9 m, (d) active nodes are disconnected with R = 9 m, (e) network is connected before node scheduling with R = 12 m and (f) active nodes are disconnected with R = 12 m.

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759

Table 1 The number of network topologies with connectivity maintenance after coverage preserving sensing-scheduling (N nodes in a 100 · 100 m2 region, communication range R = 10 m) N

200 250 300 350 400 450 500 550

R/r 1.0

1.1

1.2

1.3

1.4

1.5

1.6

1.7

1.8

1.9

2.0

2.1

2.2

670 679 648 699 634 656 666 674

813 794 794 812 784 803 785 801

879 901 896 885 890 887 888 885

955 971 957 954 952 960 953 955

982 984 980 985 989 982 978 987

997 994 996 997 997 995 991 998

1000 995 996 1000 998 999 999 998

999 999 1000 1000 1000 1000 1000 1000

1000 1000 1000 1000 1000 1000 1000 1000

1000 1000 1000 1000 1000 1000 1000 1000

1000 1000 1000 1000 1000 1000 1000 1000

1000 1000 1000 1000 1000 1000 1000 1000

1000 1000 1000 1000 1000 1000 1000 1000

a network topology with 350 nodes uniform randomly placed in a 100-by-100-m region. When the sensing range is 6 m and the original system sensing coverage is shown as Fig. 9(a). The modified coverage-preserving node scheduling algorithm in [6] identifies some inactive nodes as marked in Fig. 9(b) while maintaining the system sensing coverage is unchanged. Fig. 9(d) shows that the connectivity among active nodes is destroyed with the communication range is 1.5 times of the sensing range. While in the same sensing configuration, if the communication range is twice the size of the sensing range, the connectivity is still maintained as illustrated in Fig. 9(f). Energy saving can be achieved by communicating upon the simplified network graph with a lower node density and lower link density as shown in Fig. 9(f) and by monitoring the environments with less active nodes as shown in Fig. 9(b), compared with the original network graph. We also investigate the impact of the ratio of communication range to sensing range on the relationship between connectivity maintenance and coverage preservation. The networks we study have a sensing density from average 1.6 nodes per sensing area to 17.3 nodes per sensing area, which are obtained by varying the deployed node number from 200 to 550 and varying the size of the sensing range based on a certain ratio to a fixed communication range as 10 m. For each configuration, we generate 1000 random network topologies that are original connected. Among these 1000 network topologies, those maintaining connectivity after coverage preserving sensing-scheduling are counted. The results are listed in Table 1. Consistent with our expectation, the smaller the ratio of the communication range to the sensing range is, the lower the connectivity possibility is. However, as shown the data, the lower bound of the ratio for connectivity maintenance seems to be 1.8 instead of 2.0. That is because we just run 1000 network topologies for each configuration and the scenario illustrated in Fig. 7 is a rare and extreme situation in those networks with a very high node density. Furthermore, from the table, we observe that node density seems to have no significant impact on connectivity possibility when the ratio of communication range to sensing range is fixed. Approximating the connectivity possibility based on a given ratio of communication range to sensing range can be one of our future works.

7. Conclusion In this paper, we provided complete proof: ‘‘the communication range is twice of the sensing range’’ is the sufficient condition and the tight lower bound to ensure that complete coverage preservation implies connectivity among active nodes if the original network topology (consisting of all the deployed nodes) is connected. The significance of the above conclusion is that it enables us to focus on sensing domain when connectivity and coverage are both required, therefore greatly simplifies the safe integration of activity scheduling in both domains. We also extend the result for k-degree by proving that: ‘‘the communication

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Di Tian received the B.S. in Computer Science from Nankai University, Tianjin, China, in 1996 and the M.S. in Computer Engineering from Beijing University of Posts & Telecommunication, Beijing, China in 1999. From April 1999 to December 2000, she worked at Bell Lab Innovations, Lucent China Co. Ltd. as a member of technical staff. From July 1999 to December 1999, she was an intern at Kenan Systems Co., Boston, MA. She is currently pursuing the Ph.D., degree at School of Information Technology and Engineering, University of Ottawa. Her research interests include wireless sensor network and mobile ad hoc network.

Nicolas D. Georganas, OOnt, FIEEE, FRSC, FCAE, FEIC is Distinguished University Professor and Canada Research Chair in Information Technology at the School of Information Technology and Engineering, University of Ottawa. He received the Dipl. Ing. degree in Electrical Engineering from the National Technical University of Athens, Greece, in 1966 and the Ph.D., in Electrical Engineering (Summa cum Laude) from the University of Ottawa in 1970. He has published over 300 technical papers and is co-author of the book ‘‘Queueing Networks––Exact Computational Algorithms: A Unified Theory by Decomposition and Aggregation’’, MIT Press, 1989. He has received research grants and contracts totaling more than $51 million and has supervised more than 175 researchers, among which 90 graduate students (25 Ph.D., 65 MASc) and 18 PostDocs. In 1990, he was elected Fellow of IEEE. In 1994, he was elected Fellow of the Engineering Institute of Canada. In 1995, he was co-recipient of the IEEE INFOCOMÕ95 Prize Paper Award. In 1997, he was inducted as Fellow in the Canadian Academy of Engineering and Fellow of the Royal Society of Canada. In 1998, he was selected as the University of Ottawa Researcher of the Year and also received the University 150th Anniversary Medal for Research. In 1999, he was awarded the Thomas W. Eadie Medal of the Royal Society of Canada, funded by Bell Canada, for his contributions to Canadian and International telecommunications. In 2000, he received the A.G.L. McNaughton Gold Medal and Award for 1999–2000, the highest distinction of IEEE Canada; the Julian C. Smith Medal of the Engineering Institute of Canada; the OCRI PresidentÕs Award (jointly with Dr. Samy Mahmoud) for the creation of the National Capital Institute of Telecommunications (NCIT); the Bell Canada Forum Award from the Corporate-Higher Education Forum, the Researcher Achievement Award, from the TeleLearning Network of Centres of Excellence and a Canada Research Chair in Information Technology. In 2001, he was appointed Distinguished University Professor of the University of Ottawa and he was also received the Order of Ontario, the provinceÕs highest and most prestigious honour. In 2002, he received the Killam Prize for Engineering, CanadaÕs most distinguished award for outstanding career achievements.