Finding a small dominating set is one of the most fundamental problems of traditional graph theory. In this paper, we present a new fully distributed approximation algorithm based on LP relaxation techniques. For an arbitrary parameter k and maximum degree #, our algorithm computes a dominating set of expected size O k# log #|DSOPT rounds where each node has to send O k messages of size O(log #). This is the first algorithm which achieves a non-trivial approximation ratio in a constant number of rounds.

this article, we review some of the characteristic features of ad hoc networks, formulate problems and survey research work done in the area. We focus on two basic problem domains: topology control, the problem of computing and maintaining a connected topology among the network nodes, and routing. This article is not intended to be a comprehensive survey on ad hoc networking. The choice of the problems discussed in this article are somewhat biased by the research interests of the author

In this paper we study a model for ad-hoc networks close enough to reality as to represent existing networks, being at the same time concise enough to promote strong theoretical results. The Quasi Unit Disk Graph model contains all edges shorter than a parameter d between 0 and 1 and no edges longer than 1. We show that -- in comparison to the cost known on Unit Disk Graphs -- the complexity results in this model contain the additional factor 1/d². We prove that in Quasi Unit Disk Graphs flooding is an asymptotically message-optimal routing technique, provide a geometric routing algorithm being more efficient above all in dense networks, and show that classic geometric routing is possible with the same performance guarantees as for Unit Disk Graphs if d 1/ # 2.

Topology control in ad-hoc networks tries to lower node energy consumption by reducing transmission power and by confining interference, collisions and consequently retransmissions. Commonly low interference is claimed to be a consequence to sparseness of the resulting topology. In this paper we disprove this implication. In contrast to most of the related work---claiming to solve the interference issue by graph sparseness without providing clear argumentation or proofs---, we provide a concise and intuitive definition of interference. Based on this definition we show that most currently proposed topology control algorithms do not effectively constrain interference. Furthermore we propose connectivity-preserving and spanner constructions that are interference-minimal.

Abstract. The efficient subdivision of a sensor network into uniform, mostly non-overlapping clusters of physically close nodes is an important building block in the design of efficient upper layer network functions such as routing, broadcast, data aggregation, and query processing. We present ACE, an algorithm that results in highly uniform cluster formation that can achieve a packing efficiency close to hexagonal close-packing. By using the self-organizing properties of three rounds of feedback between nodes, the algorithm induces the emergent formation of clusters that are an efficient cover of the network, with significantly less overlap than the clusters formed by existing algorithms. The algorithm is scale-independent — it completes in time proportional to the deployment density of the nodes regardless of the overall number of nodes in the network. ACE requires no knowledge of geographic location and requires only a small constant amount of communications overhead. 1

Achieving a global goal based on local information is challenging, especially in complex and large-scale networks such as the Internet or even the human brain. In this paper, we provide an almost tight classification of the possible trade-off between the amount of local information and the quality of the global solution for general covering and packing problems. Specifically, we give a distributed algorithm using only small messages which obtains an (ρ∆) 1/k-approximation for general covering and packing problems in time O(k 2), where ρ depends on the LP’s coefficients. If message size is unbounded, we present a second algorithm that achieves an O(n 1/k) approximation in O(k) rounds. Finally, we prove that these algorithms are close to optimal by giving a lower bound on the approximability of packing problems given that each node has to base its decision on information from its k-neighborhood. 1

The XTC ad-hoc network topology control algorithm introduced in this paper shows three main advantages over previously proposed algorithms. First, it is extremely simple and strictly local. Second, it does not assume the network graph to be a Unit Disk Graph; XTC proves correct also on general weighted network graphs. Third, the algorithm does not require availability of node position information. Instead, XTC operates with a general notion of order over the neighbors' link qualities. In the special case of the network graph being a Unit Disk Graph, the resulting topology proves to have bounded degree, to be a planar graph, and---on average-case graphs---to be a good spanner.

Motivated by routing issues in ad hoc networks, we present polylogarithmic-time distributed algorithms for two problems. Given a network, we first show how to compute connected and weakly connected dominating sets whose size is at most O(log #) times optimal, # being the maximum degree of the input network. This is best-possible if NP ] and if the processors are limited to polynomial-time computation. We then show how to construct dominating sets which satisfy the above properties, as well as the "low stretch" property that any two adjacent nodes in the network have their dominators at a distance of at most O(log n) in the network. (Given a dominating set S, a dominator of a vertex u is any v S such that the distance between u and v is at most one.) We also show our time bounds to be essentially optimal.

A newly deployed multi-hop radio network is unstructured and lacks a reliable and e#cient communication scheme. In this paper, we take a step towards analyzing the problems existing during the initialization phase of ad hoc and sensor networks. Particularly, we model the network as a multihop quasi unit disk graph and allow nodes to wake up asynchronously at any time. Further, nodes do not feature a reliable collision detection mechanism, and they have only limited knowledge about the network topology. We show that even for this restricted model, a good clustering can be computed e#ciently. Our algorithm e#ciently computes an asymptotically optimal clustering. Based on this algorithm, we describe a protocol for quickly establishing synchronized sleep and listen schedule between nodes within a cluster. Additionally, we provide simulation results in a variety of settings.

The efficiency of a communication network depends not only on its control protocols, but also on its topology. We propose a distributed topology management algorithm that constructs and maintains a backbone topology based on a minimal dominating set (MDS) of the network. According to this algorithm, each node determines the membership in the MDS for itself and its one-hop neighbors based on two-hop neighbor information that is disseminated among neighboring nodes. The algorithm then ensures that the members of the MDS are connected into a connected dominating set (CDS), which can be used to form the backbone infrastructure of the communication network for such purposes as routing. The correctness of the algorithm is proven, and the efficiency is compared with other topology management heuristics using simulations. Our algorithm shows better behavior and higher stability in ad hoc networks than prior algorithms.