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.

Due to the limited resources available in the wireless ad hoc networking nodes, the scalability is crucial for network operations. One effective approach is to maintain only a sparse spanner of a linear number of links while still preseving the power-efficient route for any pair of nodes. For any spanner #, its power stretch factor is defined as the maximum ratio of the minimum power needed to support any link in this spanner to the least necessary. In this paper, we first consider several wellknown proximity graphs including relative neighborhood graph, Gabriel graph and Yao graph. These graphs are sparse and can be constructed locally in an efficient way. We show that the power stretch factor of Gabriel graph is always one, and the power stretch factor of Yao graph is bounded by a constant while the power stretch factor of relative neighborhood graph could be as large as the network size minus one. Notice that all of these graphs do not have constant degrees. We further propose another sparse spanner that has both constant degree and constant power stretch factor. An efficient local algorithm is presented for the construction of this spanner. Keywords--- Wireless ad hoc networks, topology control, power consumption, network optimization. I.

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.

Nodes in sensor networks often encounter spatially-correlated contention, where multiple nodes in the same neighborhood all sense an event they need to transmit information about. Furthermore, in many sensor network applications, it is sufficient if a subset of the nodes that observe the same event report it. We show that traditional carrier-sense multiple access (CSMA) protocols like 802.11 do not handle the first constraint adequately, and do not take advantage of the second property, leading to degraded latency and throughput as the network scales in size.

We present a new algorithm for routing of messages in ad-hoc networks where the nodes are energy-constrained. The routing objective is to maximize the total number of messages that can be successfully sent over the network without knowing any information regarding future message arrivals or message generation rates. From a theoretical perspective, we show that if admission control of messages is permitted, then the worst-case performance of our algorithm is within a factor of O(log(network size)) of the best achievable solution. In other words, our algorithm achieves a logarithmic competitive ratio. Our approach provides sound theoretical backing for several observations that have been made by previous researchers. From a practical perspective, we show by extensive simulations that the performance of the algorithm is very good even in the absence of admission control (the admission control being necessary only to prove the competitive ratio result), and that it also performs better than previously proposed algorithms for other suggested metrics such as network lifetime maximization. Our algorithm uses a single shortest path computation, and is amenable to efficient implementation. We also evaluate by simulations the performance impact of inexact knowledge of residual battery energy, and the impact of energy drain due to dissemination of residual energy information.

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.

Abstract—In this paper, we investigate the impact of variable-range transmission power control on the physical and network connectivity, on network capacity, and on power savings in wireless multihop networks. First, using previous work by Steele [18], we show that, for a path attenuation factor 2, the average range of links in a planar random network of Am2 having n nodes is c ffiffiffi p A n 1. We show that this average range is approximately half the range obtained when common-range transmission control is used. Combining this result and previous work by Gupta and Kumar [8], we derive an expression for the average traffic carrying capacity of variable-range-based multihop networks. For 2, we show that this capacity remains constant even when more nodes are added to the network. Second, we derive a model that approximates the signaling overhead of a routing protocol as a function of the transmission range and node mobility for both route discovery and route maintenance. We show that there is an optimum setting for the transmission range, not necessarily the minimum, which maximizes the capacity available to nodes in the presence of node mobility. The results presented in this paper highlight the need to design future MAC and routing protocols for wireless ad hoc and sensor networks based, not on common-range which is prevalent today, but on variable-range power control. Index Terms—Multihop networks, ad hoc networks, traffic capacity, network connectivity, power savings. Ç 1

Greedy geographic routing is attractive in wireless sensor networks due to its e#ciency and scalability. However, greedy geographic routing may incur long routing paths or even fail due to routing voids on random network topologies. We study greedy geographic routing in an important class of wireless sensor networks that provide sensing coverage over a geographic area (e.g., surveillance or object tracking systems). Our geometric analysis and simulation results demonstrate that existing greedy geographic routing algorithms can successfully find short routing paths based on local states in sensing-covered networks. In particular, we derive theoretical upper bounds on the network dilation of sensing-covered networks under greedy geographic routing algorithms. Furthermore, we propose a new greedy geographic routing algorithm called Bounded Voronoi Greedy Forwarding (BVGF) that allows sensing-covered networks to achieve an asymptotic network dilation lower than 4.62 as long as the communication range is at least twice the sensing range. Our results show that simple greedy geographic routing is an e#ective routing scheme in many sensing-covered networks.