# Local Approximation Schemes for Topology Control - Computer Science > Data Structures and Algorithms

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Abstract: This paper presents a distributed algorithm on wireless ad-hoc networks thatruns in polylogarithmic number of rounds in the size of the network andconstructs a linear size, lightweight, 1+\epsilon-spanner for any given\epsilon > 0. A wireless network is modeled by a d-dimensional \alpha-quasiunit ball graph \alpha-UBG, which is a higher dimensional generalization ofthe standard unit disk graph UDG model. The d-dimensional \alpha-UBG modelgoes beyond the unrealistic flat world- assumption of UDGs and also takesinto account transmission errors, fading signal strength, and physicalobstructions. The main result in the paper is this: for any fixed \epsilon > 0,0 < \alpha \le 1, and d \ge 2, there is a distributed algorithm running inO\log n \log^* n communication rounds on an n-node, d-dimensional \alpha-UBGG that computes a 1+\epsilon-spanner G- of G with maximum degree \DeltaG- =O1 and total weight wG- = OwMSTG. This result is motivated by thetopology control problem in wireless ad-hoc networks and improves on existingtopology control algorithms along several dimensions. The technicalcontributions of the paper include a new, sequential, greedy algorithm withrelaxed edge ordering and lazy updating, and clustering techniques forfiltering out unnecessary edges.

Autor: Mirela Damian, Saurav Pandit, Sriram Pemmaraju

Fuente: https://arxiv.org/