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DCOSS
2008
Springer

Local PTAS for Independent Set and Vertex Cover in Location Aware Unit Disk Graphs

9 years 11 months ago
Local PTAS for Independent Set and Vertex Cover in Location Aware Unit Disk Graphs
We present the first local approximation schemes for maximum independent set and minimum vertex cover in unit disk graphs. In the graph model we assume that each node knows its geographic coordinates in the plane (location aware nodes). Our algorithms are local in the sense that the status of each node v (whether or not v is in the computed set) depends only on the vertices which are a constant number of hops away from v. This constant is independent of the size of the network. We give upper bounds for the constant depending on the desired approximation ratio. We show that the processing time which is necessary in order to compute the status of a single vertex is bounded by a polynomial in the number of vertices which are at most a constant number of vertices away from it. Our algorithms give the best possible approximation ratios for this setting. The technique which we use to obtain the algorithm for vertex cover can also be employed for constructing the first global PTAS for this pr...
Andreas Wiese, Evangelos Kranakis
Added 19 Oct 2010
Updated 19 Oct 2010
Type Conference
Year 2008
Where DCOSS
Authors Andreas Wiese, Evangelos Kranakis
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