A Constant–Factor Approximation Algorithm for Red–Blue Set Cover with Unit Disks

The main contribution of this paper is the first constant factor approximation algorithm for red-blue set cover problem with unit disks. To achieve this, we first give a polynomial time algorithm for line-separable red-blue set cover problem with unit disks. We next obtain a factor 2 approximation a...

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Bibliographic Details
Published in:Algorithmica Vol. 85; no. 1; pp. 100 - 132
Main Authors: Madireddy, Raghunath Reddy, Mudgal, Apurva
Format: Journal Article
Language:English
Published: New York Springer US 01.01.2023
Springer Nature B.V
Subjects:
Algorithm Analysis and Problem Complexity
Algorithms
Approximation
Computer Science
Computer Systems Organization and Communication Networks
Data Structures and Information Theory
Disks
Mathematical analysis
Mathematics of Computing
Polynomials
Strip
Theory of Computation
Sweep-line method
Unit disks
Strip-separable
Line-separable
Red–blue set cover
ISSN:0178-4617, 1432-0541
Online Access:Get full text
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Summary:The main contribution of this paper is the first constant factor approximation algorithm for red-blue set cover problem with unit disks. To achieve this, we first give a polynomial time algorithm for line-separable red-blue set cover problem with unit disks. We next obtain a factor 2 approximation algorithm for strip-separable red-blue set cover problem with unit disks. Finally, we obtain a constant factor approximation algorithm for red-blue set cover problem with unit disks by combining our algorithm for the strip-separable problem with the results of Ambühl et al. [ 1 ]. Our methods involve a novel decomposition of the optimal solution to line-separable problem into blocks with special structure and extensions of the sweep-line technique of Erlebach and van Leeuwen [ 9 ].
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ISSN:0178-4617
1432-0541
DOI:10.1007/s00453-022-01012-z