Energy conservation is a critical issue in designing wireless ad hoc networks, as the nodes are powered by batteries only. Given a set of wireless network nodes, the directed weighted transmission graph Gt has an edge uv if and only if node v is in the transmission range of node u and the weight of uv is typically defined as II,,vll + c for a constant 2 <_ t ~ < 5 and c> O. The minimum power topology Gm is the smallest subgraph of Gt that contains the shortest paths between all pairs of nodes, i.e., the union of all shortest paths. In this paper, we described a distributed position-based networking protocol to construct an enclosure graph G~, which is an approximation of Gin. The time complexity of each node u is O(min(dG ~ (u)dG ~ (u), dG ~ (u) log dG ~ (u))), where dc(u) is the degree of node u in a graph G. The space required at each node to compute the minimum power topology is O(dG ~ (u)). This improves the previous result that computes Gm in O(dG, (u) a) time using O(dGt(U) 2) spaces. We also show that the average degree dG,(u) is usually a constant, which is at most 6. Our result is first developed for stationary network and then extended to mobile networks. I.

Several localized routing protocols [1] guarantee the delivery of the 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 in between two nodes exist only if the distance in between them is at most the maximum transmission range.

Sensor networks pose a number of challenging conceptual and optimization problems such as location, deployment, and tracking [1]. One of the fundamental problems in sensor networks is the calculation of the coverage. In [1], it is assumed that the sensor has the uniform sensing ability. In this paper, we give efficient distributed algorithms to optimally solve the best-coverage problem raised in [1]. Here, we consider the 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 bestcoverage -path with the least energy consumption. We also consider how to find an optimum best-coverage-path that travels a small distance. In addition, we justify the correctness of the method proposed in [1] that uses the Delaunay triangulation to solve the best coverage problem. Moreover, we show that the search space of the best coverage problem can be confined to the relative neighborhood graph, which can be constructed locally.

We propose a novel localized algorithm that constructs a bounded degree and planar spanner for wireless ad hoc networks modeled by unit disk graph (UDG). Every node only has to know its 2-hop neighbors to find the edges in this new structure. Our method applies the Yao structure on the local Delaunay graph [21] in an ordering that are computed locally. This new structure has the following attractive properties: (1) it is a planar graph; (2) its node degree is bounded from above by a positive constant 19 + ⌈ 2π α ⌉; (3) it is a t-spanner (given any two nodes u and v, there is a path connecting them in the structure such that its length is no more than t ≤ max { π α,πsin 2 2 +1}·Cdel times of the shortest path in UDG); (4) it can be constructed locally and is easy to maintain when the nodes move around; (5) moreover, we show that the total communication cost is O(n), where n is the number of wireless nodes, and the computation cost of each node is at most O(d log d), where d is its 2-hop neighbors in the original unit disk graph. Here Cdel is the spanning ratio of the Delaunay triangulation, which is at most 4 √ 3 9 π. And the adjustable parameter α satisfies 0 <α<π/3. In addition, experiments are conducted to show this topology is efficient in practice, compared with other well-known topologies used in wireless ad hoc networks. Previously, only centralized method [5] of constructing bounded degree planar spanner is known, with degree bound 27 and spanning ratio t ≃ 10.02. The distributed implementation of their centralized method takes O(n 2) communications in the worst case. No localized methods were known previously for constructing bounded degree planar spanner.

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.

This paper investigate fault tolerance for wireless ad hoc networks. We consider a large-scale of wireless networks whose nodes are distributed randomly in a unit-area square region. Given n wireless nodes V , each with transmission range rn , the wireless networks are often modeled by graph G(V,rn ) in which two nodes are connected if their Euclidean distance is no more than rn .

dimensional plane. Each wireless node has an omnidirectional antenna. This is attractive for a single We consider how to construct power wireless ad mission of a node can be received by many nodes within hoc networks. We propose two different methods its vicinity. In the most common power-attenuation several well-known proximity graphs including Gabriel graph and Yao which can be constructed locally and Firstly, we combine the Gabriel and model, the power needed to support a link is where is the distance between and v, is a real constant between 2 and 4 dependent on the wireless transmission environment. By a proper scaling, we sume that all nodes have the maximum transmission range equal to one unit. These wireless nodes define a unit disk graph in which there is an edge between two nodes if and only if their Euclidean distance is at most one. The size of the unit disk graph could be large as the square order of the number of network nodes. Given a unicasting or multicasting request, the routing problem is to find a route whose energy consumption is within a small constant factor of the optimum route. Notice that the time complexity of computing the shortest path connecting two nodes is the Yao structure. The constructed topology has at most edges and each node has a bounded out-degree.

We present a network initialization algorithm for wireless networks with distributed intelligence. Each node (agent) has only local, incomplete knowledge and it must make local decisions to meet a predefined global objective. Our objective is to use power control to establish a topology based on the relative neighborhood graph which has good overall performance in terms of power usage, low interference, and reliability. I.

We study topology control in heterogeneous wireless ad hoc networks, where mobile hosts may have different maximum transmission powers and two nodes are connected iff they are within the maximum transmission range of each other. We present several strategies that all wireless nodes self-maintain sparse and power efficient topologies in heterogeneous network environment with low communication cost. The first structure is sparse and can be used for broadcasting. While the second structure keeps the minimum power consumption path, and the third structure is a length and power spanner with a bounded degree. Both the second and third structures are power efficient and can be used for unicast. Here a structure is power efficient if the total power consumption of the least cost path connecting any two nodes in it is no more than a small constant factor of that in the original heterogeneous communication graph. All our methods use at most O(n) total messages, where each message has O(log n) bits.

Abstract. Topology control in wireless ad hoc networks is to select a subgraph of the communication graph (when all nodes use their maximum transmission range) with some properties for energy conservation. In this paper, we propose two novel localized topology control methods for homogeneous wireless ad hoc networks. Our first method constructs a structure with the following attractive properties: power efficient, bounded node degree, and planar. Its power stretch factor is at most ρ = 1 1−(2 sin π k)β, and each node only has to maintain at most k + 5 neighbors where the integer k> 6 is an adjustable parameter, and β is a real constant between 2 and 5 depending on the wireless transmission environment. It can be constructed and maintained locally and dynamically. Moreover, by assuming that the node ID and its position can be represented in O(log n) bits each for a wireless network of n nodes, we show that the structure can be constructed using at most 24n messages, where each message is O(log n) bits. Our second method improves the degree bound to k, relaxes the theoretical power span-ning ratio to ρ = √ 2 β 1−(2 √ 2 sin π, where k> 8 is an adjustable parameter, and keeps all other)β k properties. We show that the second structure can be constructed using at most 3n messages, where each message has size of O(log n) bits. We also experimentally evaluate the performance of these new energy efficient network topologies. The theoretical results are corroborated by the simulations: these structures are more efficient in practice, compared with other known structures used in wireless ad hoc networks and are easier to construct. In addition, the power assignment based on our new structures shows low energy cost and small interference at each wireless node.