Free Online Productivity Tools
i2Speak
i2Symbol
i2OCR
iTex2Img
iWeb2Print
iWeb2Shot
i2Type
iPdf2Split
iPdf2Merge
i2Bopomofo
i2Arabic
i2Style
i2Image
i2PDF
iLatex2Rtf
Sci2ools

SWAT

2010

Springer

2010

Springer

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...

Added |
11 Jul 2010 |

Updated |
11 Jul 2010 |

Type |
Conference |

Year |
2010 |

Where |
SWAT |

Authors |
Imran A. Pirwani, Mohammad R. Salavatipour |

Comments (0)