A local distributed algorithm to approximate MST in unit disc graphs

Authors:
Krzysztof Krzywdziński
Affiliations:
Faculty of Mathematics and Computer Science, Adam Mickiewicz University, Poznań, Poland
Venue:
FCT'09 Proceedings of the 17th international conference on Fundamentals of computation theory
Year:
2009

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Abstract

We present a new distributed algorithm, which finds a good approximation of the Minimum Spanning Tree in the Unit Disc Graphs. Our algorithm, in O(d2) synchronous rounds, where d is an input parameter, finds a subgraph H of the Unit Disc Graph G which contains a Minimum Spanning Tree of G. Moreover, H is planar, does not contain cycles of weight smaller than d/3 and the weight of H is (1 + O(1/d)) approximation of the weight of the Minimum Spanning Tree of G.