Approximation algorithms for maximum independent set of a unit disk graph

Gautam K. Das, Minati De, Sudeshna Kolay, Subhas C. Nandy, Susmita Sur-Kolay

Research output: Contribution to journalArticlepeer-review

15 Scopus citations

Abstract

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 (n log n) 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+1/k)2|OPT| in O (k4nσk log k + n log n) time and O (n + k log k) space, where OPT is the subset of disks in an optimal solution and σk ≤ 7k/3 + 2. For a penny graph, the proposed PTAS produces a solution of size 1/(1+1/k)|OPT | in O (22σk nk + n log n) time using O (2σk + n) space.

Original languageEnglish
Pages (from-to)439-446
Number of pages8
JournalInformation Processing Letters
Volume115
Issue number3
DOIs
StatePublished - 1 Jan 2015
Externally publishedYes

Keywords

  • Approximation algorithms
  • Computational geometry
  • Maximum independent set
  • PTAS
  • Unit disk graph

ASJC Scopus subject areas

  • Theoretical Computer Science
  • Signal Processing
  • Information Systems
  • Computer Science Applications

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