ISAAC 2009: Algorithms and Computation pp 45-54

# Practical Discrete Unit Disk Cover Using an Exact Line-Separable Algorithm

• Francisco Claude
• Reza Dorrigiv
• Stephane Durocher
• Robert Fraser
• Alejandro López-Ortiz
• Alejandro Salinger
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 5878)

## Abstract

Given m unit disks and n points in the plane, the discrete unit disk cover problem is to select a minimum subset of the disks to cover the points. This problem is NP-hard [11] and the best previous practical solution is a 38-approximation algorithm by Carmi et al. [4]. We first consider the line-separable discrete unit disk cover problem (the set of disk centres can be separated from the set of points by a line) for which we present an O(m 2 n)-time algorithm that finds an exact solution. Combining our line-separable algorithm with techniques from the algorithm of Carmi et al. [4] results in an O(m 2 n 4) time 22-approximate solution to the discrete unit disk cover problem.

## Keywords

Unit Disk Simplification Rule Disk Centre Minimum Cardinality Unit Disk Graph
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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## Authors and Affiliations

• Francisco Claude
• 1
• Reza Dorrigiv
• 1
• Stephane Durocher
• 2
• Robert Fraser
• 1
• Alejandro López-Ortiz
• 1
• Alejandro Salinger
• 1
1. 1.Cheriton School of Computer ScienceUniversity of WaterlooWaterlooCanada
2. 2.Department of Computer ScienceUniversity of ManitobaWinnipegCanada