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.

In this paper we present GOAFR, a new geometric ad-hoc routing algorithm combining greedy and face routing. We evaluate this algorithm by both rigorous analysis and comprehensive simulation. GOAFR is the first ad-hoc algorithm to be both asymptotically optimal and average-case efficient. For our simulations we identify a network density range critical for any routing algorithm. We study a dozen of routing algorithms and show that GOAFR outperforms other prominent algorithms, such as GPSR or AFR.

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.

In this paper, we study an algorithmic model for wireless ad hoc and sensor networks that aims to be sufficiently close to reality as to represent practical realworld networks while at the same time being 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 for unit disk graphs-the complexity results of geographic routing in this model contain the additional factor 1/d 2 . We prove that in quasi unit disk graphs flooding is an asymptotically message-optimal routing technique, we provide a geographic routing algorithm being most efficient in dense networks, and we show that classic geographic routing is possible with the same asymptotic performance guarantees as for unit disk graphs if d ! 1=ffiffi ffi 2 p .

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