We consider the problem of adjusting the transmit powers of nodes in a multihop wireless network (also called an ad hoc network) to create a desired topology. We formulate it as a constrained optimization problem with two constraints - connectivity and biconnectivity, and one optimization objective - maximum power used. We present two centralized algorithms for use in static networks, and prove their optimality. For mobile networks, we present two distributed heuristics that adaptively adjust node transmit powers in response to topological changes and attempt to maintain a connected topology using minimum power. We analyze the throughput, delay, and power consumption of our algorithms using a prototype software implementation, an emulation of a power-controllable radio, and a detailed channel model. Our results show that the performance of multihop wireless networks in practice can be substantially increased with topology control.

Abstract — The topology of wireless multihop ad hoc networks can be controlled by varying the transmission power of each node. We propose a simple distributed algorithm where each node makes local decisions about its transmission power and these local decisions collectively guarantee global connectivity. Specifically, based on the directional information, a node grows it transmission power until it finds a neighbor node in every direction. The resulting network topology increases network lifetime by reducing transmission power and reduces traffic interference by having low node degrees. Moreover, we show that the routes in the multihop network are efficient in power consumption. We give an approximation scheme in which the power consumption of each route can be made arbitrarily close to the optimal by carefully choosing the parameters. Simulation results demonstrate significant performance improvements. I.

We can control the topology of a multi-hop wireless network by varying the transmission power at each node. The life-time of such networks depends on battery power at each node. This paper presents a distributed fault-tolerant topology control algorithm for minimum energy consumption in these networks. More precisely, we present algorithms which preserve the connectivity of a network upon failing of, at most, k nodes (k is constant) and simultaneously minimize the transmission power at each node to some extent. In addition, we present simulations to support the effectiveness of our algorithm. We also demonstrate some optimizations to further minimize the power at each node. Finally, we show how our algorithms can be extended to 3-dimensions.

The topology of a wireless multi-hop network can be controlled by varying the transmission power at each node. In this paper, we give a detailed analysis of a cone-based distributed topology control algorithm. This algorithm does not assume that nodes have GPS information available; rather it depends only on directional information. Roughly speaking, the basic idea of the algorithm is that a node u transmits with the minimum power p u,# required to ensure that in every cone of degree # around u, there is some node that u can reach with power p u,# . We show that taking # = 5#/6 is a necessary and su#cient condition to guarantee that network connectivity is preserved. More precisely, if there is a path from s to t when every node communicates at maximum power then, if # 5#/6, there is still a path in the smallest symmetric graph G # containing all edges (u, v) such that u can communicate with v using power p u,# . On the other hand, if # > 5#/6, # This is a revised and extended version of "Analysis of a cone-based topology control algorithm for wireless multi-hop networks", which appeared in Proceedings of ACM Principles of Distributed Computing (PODC), 2001, and includes results from "Distributed topology control for power e#cient operation in multihop wireless ad hoc networks", by R. Wattenhofer, L. Li, P. Bahl, and Y. M. Wang, which appeared in Proceedings of IEEE INFOCOM, 2001.

The topology of a wireless multi-hop network can be controlled by varying the transmission power at each node. In general, it is not energy efficient to use the communication network where every node transmits with maximum power. For energy efficient operations, it is desirable to have a subnetwork that preserves a minimum-energy path between every pair of nodes (where a minimum-energy path is one that allows messages to be transmitted with a minimum use of energy). In this paper, we first identify conditions that are necessary and sufficient for a subnetwork of to preserve this property. Using this characterization, we then propose an efficient topologycontrol algorithm that, given a communication network, computes a subnetwork that it preserves at least one minimumenergy path between every pair of nodes. We also propose an energy-efficient reconfiguration protocol that maintains this minimum-energy path property as the network topology changes dynamically. We demonstrate the performance improvements of our algorithm over other existing topology-control algorithms through simulation.

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