Minimum clique partition in unit disk graphs
نویسندگان
چکیده
The minimum clique partition (MCP) problem is that of partitioning the vertex set of a given graph into a minimum number of cliques. Given n points in the plane, the corresponding unit disk graph (UDG) has these points as vertices, and edges connecting points at distance at most 1. MCP in unit disk graphs is known to be NP-hard and several constant factor approximations are known, including a recent PTAS. We present two improved approximation algorithms for minimum clique partition in unit disk graphs with a realization: (I) A polynomial time approximation scheme (PTAS) running in time nO(1/ε 2). This improves on a previous PTAS with nO(1/ε ) running time [23]. (II) A randomized quadratic-time algorithm with approximation ratio 2.16. This improves on a ratio 3 algorithm with O(n2) running time [7].
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عنوان ژورنال:
- Graphs and Combinatorics
دوره 27 شماره
صفحات -
تاریخ انتشار 2011