Approximation algorithms for maximum independent set of a unit disk graph
We propose a 2-approximation algorithm for the maximum independent set problem for a unit disk graph. The time and space complexities are O(n3) and O(n2), respectively. For a penny graph, our proposed 2-approximation algorithm works in O(nlogn) time using O(n) space. We also propose a polynomial-ti...
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Veröffentlicht in: | Information processing letters 2015-03, Vol.115 (3), p.439-446 |
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Sprache: | eng |
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Zusammenfassung: | We propose a 2-approximation algorithm for the maximum independent set problem for a unit disk graph. The time and space complexities are O(n3) and O(n2), respectively. For a penny graph, our proposed 2-approximation algorithm works in O(nlogn) time using O(n) space. We also propose a polynomial-time approximation scheme (PTAS) for the maximum independent set problem for a unit disk graph. Given an integer k>1, it produces a solution of size 1(1+1k)2|OPT| in O(k4nσklogk+nlogn) time and O(n+klogk) space, where OPT is the subset of disks in an optimal solution and σk≤7k3+2. For a penny graph, the proposed PTAS produces a solution of size 1(1+1k)|OPT| in O(22σknk+nlogn) time using O(2σk+n) space.
•A 2-factor approximation for computing the maximum independent set of unit disk graph is proposed. It runs in O(n3) time and O(n2) space.•A similar technique works for penny graph in O(nlogn) time and produces a 2-approximation result.•Efficient PTAS are proposed for computing the maximum independent set of unit disk graph and penny graph. |
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ISSN: | 0020-0190 1872-6119 |
DOI: | 10.1016/j.ipl.2014.11.002 |