In all-wireless networks a crucial problem is to minimize energy consumption, as in most cases the nodes are batteryoperated. We focus on the problem of power-optimal broadcast, for which it is well known that the broadcast nature of the radio transmission can be exploited to optimize energy consumption. Several authors have conjectured that the problem of power-optimal broadcast is NP-complete. We provide here a formal proof, both for the general case and for the geometric one; in the former case, the network topology is represented by a generic graph with arbitrary weights, whereas in the latter a Euclidean distance is considered. We then describe a new heuristic, Embedded Wireless Multicast Advantage. We show that it compares well with other proposals and we explain how it can be distributed. Categories and Subject Descriptors

supported by NSF CCR-0311174. Abstract — Topology control has been well studied in wireless ad hoc networks. However, only a few topology control methods take into account the low interference as a goal of the methods. Some researchers tried to reduce the interference by lowering node energy consumption (i.e. by reducing the transmission power) or by devising low degree topology controls, but none of those protocols can guarantee low interference. Recently, Burkhart et al. [?] proposed several methods to construct topologies whose maximum link interference is minimized while the topology is connected or is a spanner for Euclidean length. In this paper we give algorithms to construct a network topology for wireless ad hoc network such that the maximum (or average) link (or node) interference of the topology is either minimized or approximately minimized. Index Terms — Topology control, interference, wireless ad hoc networks.

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Abstract. Used for topology control in ad-hoc wireless networks, Power Assignment is a family of problems, each defined by a certain connectivity constraint (such as strong connectivity) The input consists of a directed complete weighted graph G = (V; c). The power of a vertex u in a directed spanning subgraph H is given by pH(u) = maxuv2E(H) c(uv). The power of H is given by p(H) = P u2V pH(u), Power Assignment seeks to minimize p(H) while H satisfies the given connectivity constraint. We

Energy conservation is a critical issue in ad hoc wireless networks for node and network life since the nodes are powered by batteries only. One major approach for...

One of the main benefits of power controlled ad-hoc wireless networks is their ability to vary the range in order to reduce the power consumption. Minimizing energy consumption is crucial on such kind of networks since, typically, wireless devices are portable and benefit only of limited power resources. On the other hand, the network must have a sufficient degree of connectivity in order to guarantee fast and efficient communication. These two aspects yield a class of fundamental optimization problems, denoted as range assignment problems, that have been the subject of several works in the area of wireless network theory. The primary aim of this paper is to describe the most important recent advances on this class of problems. Rather than completeness, the paper will try to provide results and techniques that seem to be the most promising to address the several important related problems which are still open. Discussing such related open problems are indeed our other main goal.

We address the problem of energy-efficient reliable wireless communication in the presence of unreliable or lossy wireless link layers in multi-hop wireless networks. Prior work [1] has provided an optimal energy efficient solution to this problem for the case where link layers implement perfect reliability. However, a more common scenario — a link layer that is not perfectly reliable, was left as an open problem. In this paper we first present two centralized algorithms, BAMER and GAMER, that optimally solve the minimum energy reliable communication problem in presence of unreliable links. Subsequently we present a distributed algorithm, DAMER, that approximates the performance of the centralized algorithm and leads to significant performance improvement over existing singlepath or multi-path based techniques. Categories and Subject Descriptors

We present an overview of the recent progress of applying computational geometry techniques to solve some questions, such as topology construction and broadcasting, in wireless ad hoc networks. Treating each wireless device as a node in a two dimensional plane, we model the wireless networks by unit disk graphs in which two nodes are connected if their Euclidean distance is no more than one. We rst summarize the current status of constructing sparse spanners for unit disk graphs with various combinations of the following properties: bounded stretch factor, bounded node degree, planar, and bounded total edges weight (compared with the minimum spanning tree). Instead of constructing subgraphs by removing links, we then review the algorithms for constructing a sparse backbone (connected dominating set), i.e., subgraph from the subset of nodes. We then review some ecient methods for broadcasting and multicasting with theoretic guaranteed performance.

Computing energy efficient broadcast trees is one of the most prominent operations in wireless networks. For stations embedded in the Euclidean plane, the best analytic result known to date is a 6.33-approximation algorithm based on computing an Euclidean minimum spanning tree. We improve the analysis of this algorithm and show that its approximation ratio is 6, which matches a previously known lower bound for this algorithm.

This paper presents a distributed algorithm called LREMiT for extending the lifetime of a source-based multicast tree in wireless ad hoc networks (WANET). The lifetime of a multicast tree is the duration from the formation of the tree to the time when the first node fails due to battery energy exhaustion. L-REMiT assumes that the energy consumed to forward a packet is proportional to the forwarding distance and that WANET nodes can dynamically adjust their transmission power. The task of extending the lifetime of a multicast tree is formulated as the task of extending the lifetime of bottleneck nodes in the tree. The number of multicast packets which a bottleneck node can forward, as determined by its residual battery energy and the distance of its farthest child node, is minimum over all the nodes in the multicast tree. Lifetime of a bottleneck node is improved by reassigning its farthest children to other nodes in the tree with the goal of improving the lifetime of the multicast tree. Nodes only require information from their neighbors for refining the tree in a distributed manner. Simulation results show that L-REMiT has low overhead and performs better than BIP/MIP and EWMA algorithms.