## 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 (n^{3}) and O (n^{2}), 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 (k^{4}n^{σk 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 σ_{k} ≤ 7k/3 + 2. For a penny graph, the proposed PTAS produces a solution of size 1/(1+1/k)|OPT | in O (2^{2σk} nk + n log n) time using O (2^{σk} + n) space.

Original language | English |
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Pages (from-to) | 439-446 |

Number of pages | 8 |

Journal | Information Processing Letters |

Volume | 115 |

Issue number | 3 |

DOIs | |

State | Published - 1 Jan 2015 |

Externally published | Yes |

## 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