Peng-Jun Wan

Coverage in wireless ad hoc sensor networks

Sensor networks pose a number of challenging conceptual and optimization problems such as location, deployment, and tracking. One of the fundamental problems in sensor networks is the calculation of the coverage. In Meguerdichian et al. (2001), it is assumed that the sensor has uniform sensing ability. We provide efficient distributed algorithms to optimally solve the best-coverage problem raised in the above-mentioned article. In addition, we consider a more general sensing model: the sensing ability diminishes as the distance increases. As energy conservation is a major concern in wireless (or sensor) networks, we also consider how to find an optimum best-coverage-path with the least energy consumption and how to find an optimum best-coverage-path that travels a small distance. In addition, we justify the correctness of the method proposed above that uses the Delaunay triangulation to solve the best coverage problem and show that the search space of the best coverage problem can be confined to the relative neighborhood graph, which can be constructed locally.

Minimum-energy broadcast routing in static ad hoc wireless networks

Energy conservation is a critical issue in ad hoc wireless networks for node and network life, as the nodes are powered by batteries only. One major approach for energy conservation is to route a communication session along the routes which requires the lowest total energy consumption. This optimization problem is referred to as minimum-energy routing. While minimum-energy unicast routing can be solved in polynomial time by shortest-path algorithms, it remains open whether minimum-energy broadcast routing can be solved in polynomial time, despite the NP-hardness of its general graph version. Previously three greedy heuristics were proposed in Wieselthier et al. (2000): MST (minimum spanning tree), SPT (shortest-path tree), and BIP (broadcasting incremental power). They have been evaluated through simulations in Wieselthier et al.], but little is known about their analytical performance. The main contribution of this paper is the quantitative characterization of their performances in terms of approximation ratios. By exploring geometric structures of Euclidean MSTs, we have been able to prove that the approximation ratio of MST is between 6 and 12, and the approximation ratio of BIP is between /sup 13///sub 3/ and 12. On the other hand, the approximation ratio of SPT is shown to be at least /sup n///sub 2/, where n is the number of receiving nodes. To our best knowledge, these are the first analytical results for minimum-energy broadcasting.

Message-optimal connected dominating sets in mobile ad hoc networks

A connected dominating set (CDS) for a graph G(V,E) is a subset V1 of V, such that each node in V--V1 is adjacent to some node in V1, and V1 induces a connected subgraph. A CDS has been proposed as a virtual backbone for routing in wireless ad hoc networks. However, it is NP-hard to find a minimum connected dominating set (MCDS). Approximation algorithms for MCDS have been proposed in the literature. Most of these algorithms suffer from a very poor approximation ratio, and from high time complexity and message complexity. Recently, new distributed heuristics for constructing a CDS were developed, with constant approximation ratio of 8. These new heuristics are based on a construction of a spanning tree, which makes it very costly in terms of communication overhead to maintain the CDS in the case of mobility and topology changes.In this paper, we propose the first distributed approximation algorithm to construct a MCDS for the unit-disk-graph with a emph constant approximation ratio, and emph linear time and emph linear message complexity. This algorithm is fully localized, and does not depend on the spanning tree. Thus, the maintenance of the CDS after changes of topology guarantees the maintenance of the same approximation ratio. In this algorithm each node requires knowledge of its single-hop neighbors, and only a constant number of two-hop and three-hop neighbors. The message length is O( log n) bits.

New distributed algorithm for connected dominating set in wireless ad hoc networks

Connected dominating set (CDs) has been proposed as virtual backbone or spine of wireless ad hoc networks. Three distributed approximation algorithms have been proposed in the literature for minimum CDS. We first reinvestigate their performances. None of these algorithms have constant approximation factors. Thus these algorithms can not guarantee to generate a CDs of small size. Their message complexities can be as high as O(n/sup 2/), and their time complexities may also be as large as O(n/sup 2/) and O(n/sup 3/). We then present our own distributed algorithm that outperforms the existing algorithms. This algorithm has an approximation factor of at most 8, O(n) time complexity and O(n log n) message complexity. By establishing the /spl Omega/(n log n) lower bound on the message complexity of any distributed algorithm for nontrivial CDs, our algorithm is thus message-optimal.

Distributed construction of connected dominating set in wireless ad hoc networks

Connected dominating set (CDS) has been proposed as virtual backbone or spine of wireless ad hoc networks. Three distributed approximation algorithms have been proposed in the literature for minimum CDS. In this paper, we first reinvestigate their performances. None of these algorithms have constant approximation factors. Thus these algorithms cannot guarantee to generate a CDS of small size. Their message complexities can be as high as O(n2), and their time complexities may also be as large as O(n2) and O(n3). We then present our own distributed algorithm that outperforms the existing algorithms. This algorithm has an approximation factor of at most 8, O(n) time complexity and O(nlog n) message complexity. By establishing the Ω(nlog n) lower bound on the message complexity of any distributed algorithm for nontrivial CDS, our algorithm is thus message-optimal.

Distributed construction of a planar spanner and routing for ad hoc wireless networks

Several localized routing protocols (see Bose, P. and Morin, P., Proc. 10th Annual Int. Symp. on Algorithms and Computation ISAAC, 1999) guarantee the delivery of packets when the underlying network topology is the Delaunay triangulation of all wireless nodes. However, it is expensive to construct the Delaunay triangulation in a distributed manner. Given a set of wireless nodes, we more accurately model the network as a unit-disk graph, UDG, in which a link between two nodes exists only if the distance between them is at most the maximum transmission range. Given a graph H, a spanning subgraph G of H is a t-spanner if the length of the shortest path connecting any two points in G is no more than t times the length of the shortest path connecting the two points in H. We present a novel localized networking protocol that constructs a planar 2.5-spanner of UDG, called the localized Delaunay triangulation, as network topology. It contains all edges that are in both the UDG and the Delaunay triangulation of all wireless nodes. Our experiments show that the delivery rates of existing localized routing protocols are increased when localized Delaunay triangulation is used instead of several previously proposed topologies. The total communication cost of our networking protocol is O(n log n) bits. Moreover, the computation cost of each node u is O(d/sub u/ log d/sub u/), where d/sub u/ is the number of 1-hop neighbors of u in UDG.

Geometric spanners for wireless ad hoc networks

We propose a new geometric spanner for static wireless ad hoc networks, which can be constructed efficiently in a localized manner. It integrates the connected dominating set and the local Delaunay graph to form a backbone of the wireless network. Priori arts showed that both structures can be constructed locally with bounded communication costs. This new spanner has these following attractive properties: 1) the backbone is a planar graph, 2) the node degree of the backbone is bounded from above by a positive constant, 3) it is a spanner for both hops and length, 4) it can be constructed locally and is easy to maintain when the nodes move around, and 5) moreover, the communication cost of each node is bounded by a constant. Simulation results are also presented for studying its practical performance.

Minimum-latency aggregation scheduling in multihop wireless networks

Minimum-latency aggregation schedule (MLAS) in synchronous multihop wireless networks seeks a shortest schedule for data aggregation subject to the interference constraint. In this paper, we study MLAS under the protocol interference model in which each node has a unit communication radius and an interference radius ρ ≥ 1. All known aggregation schedules assumed ρ = 1, and the best-known aggregation latency with ρ = 1 is 23<i>R</i> + Δ - 18 where <i>R</i> and Δ are the radius and maximum degree of the communication topology respectfully. In this paper, we first construct three aggregations schedules with ρ = 1 of latency 15<i>R</i> + Δ - 4, 2<i>R</i> + <i>O</i>(log <i>R</i>) + Δ and (1 + <i>O</i>(log <i>R</i>/3√<i>R</i>)) <i>R</i> + Δ respectively. Then, we obtain two aggregation schedules with ρ > 1 by expanding the first two aggregation schedules with ρ = 1. Both aggregation schedules with ρ > 1 have latency within constant factors of the minimum aggregation latency.

Coverage by randomly deployed wireless sensor networks

One of the main applications of wireless sensor networks is to provide proper coverage of their deployment regions. A wireless sensor network k-covers its deployment region if every point in its deployment region is within the coverage ranges of at least k sensors. In this paper, we assume that the sensors are deployed as either a Poisson point process or a uniform point process in a square or disk region, and study how the probability of the k-coverage changes with the sensing radius or the number of sensors. Our results take the complicated boundary effect into account, rather than avoiding it by assuming the toroidal metric as done in the literature.

Localized Delaunay triangulation with application in ad hoc wireless networks

Several localized routing protocols guarantee the delivery of the packets when the underlying network topology is a planar graph. Typically, relative neighborhood graph (RING) or Gabriel graph (GG) is used as such planar structure. However, it is well-known that the spanning ratios of these two graphs are not bounded by any constant (even for uniform randomly distributed points). Bose et al. (1999) recently developed a localized routing protocol that guarantees that the distance traveled by the packets is within a constant factor of the minimum if Delaunay triangulation of all wireless nodes is used, in addition, to guarantee the delivery of the packets. However, it is expensive to construct the Delaunay triangulation in a distributed manner. Given a set of wireless nodes, we model the network as a unit-disk graph (UDG), in which a link uv exists only if the distance /spl par/uv/spl par/ is at most the maximum transmission range. In this paper, we present a novel localized networking protocol that constructs a planar 2 5-spanner of UDG, called the localized Delaunay triangulation (LDEL), as network topology. It contains all edges that are both in the unit-disk graph and the Delaunay triangulation of all nodes. The total communication cost of our networking protocol is O(n log n) bits, which is within a constant factor of the optimum to construct any structure in a distributed manner. Our experiments show that the delivery rates of some of the existing localized routing protocols are increased when localized Delaunay triangulation is used instead of several previously proposed topologies. Our simulations also show that the traveled distance of the packets is significantly less when the FACE routing algorithm is applied on LDEL, rather than applied on GG.