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SWAT
2010
Springer

A Weakly Robust PTAS for Minimum Clique Partition in Unit Disk Graphs

10 years 5 days ago
A Weakly Robust PTAS for Minimum Clique Partition in Unit Disk Graphs
We consider the problem of partitioning the set of vertices of a given unit disk graph (UDG) into a minimum number of cliques. The problem is NP-hard and various constant factor approximations are known, with the current best ratio of 3. Our main result is a weakly robust polynomial time approximation scheme (PTAS) for UDGs expressed with edge-lengths, it either (i) computes a clique partition or (ii) gives a certificate that the graph is not a UDG; for the case (i) that it computes a clique partition, we show that it is guaranteed to be within (1+ε) ratio of the optimum if the input is UDG; however if the input is not a UDG it either computes a clique partition as in case (i) with no guarantee on the quality of the clique partition or detects that it is not a UDG. Noting that recognition of UDG’s is NP-hard even if we are given edge lengths, our PTAS is a weakly-robust algorithm. Our algorithm can be transformed into an O log∗ n εO(1) time distributed PTAS. We consider a weigh...
Imran A. Pirwani, Mohammad R. Salavatipour
Added 11 Jul 2010
Updated 11 Jul 2010
Type Conference
Year 2010
Where SWAT
Authors Imran A. Pirwani, Mohammad R. Salavatipour
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