Efficient independent set approximation in unit disk graphs

Efficient Independent Set Approximation in Unit Disk Graphs *

Gautam Das (1) , Guilherme D. da Fonseca (2, 3) , Ramesh K Jallu

1 University of Texas at Arlington [Arlington]
2 UCA [2017-2020] - Université Clermont Auvergne [2017-2020]
3 LIMOS - Laboratoire d'Informatique, de Modélisation et d'Optimisation des Systèmes

We consider the maximum (weight) independent set problem in unit disk graphs. The high complexity of the existing polynomial-time approximation schemes motivated the development of faster constant-approximation algorithms. In this article, we present a 2.16-approximation algorithm that runs in O(n log^2 n) time and a 2-approximation algorithm that runs in O(n^2 log n) time for the unweighted version of the problem. In the weighted version, the running times increase by an O(log n) factor. Our algorithms are based on a classic strip decomposition, but we improve over previous algorithms by efficiently using geometric data structures. We also propose a PTAS for the unweighted version.

Mots clés: Maximum Independent Set; Unit Disk Graph; Approximation Algorithms; Polynomial Time Approximation Scheme

Domaines: Géométrie algorithmique [cs.CG]

Gautam Das, Guilherme D. da Fonseca, Ramesh K Jallu. Efficient independent set approximation in unit disk graphs. Discrete Applied Mathematics, 2018, ⟨10.1016/j.dam.2018.05.049⟩. ⟨hal-01893742⟩