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

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Abstract

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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Authors and Affiliations

  1. Department of Computer Science and Information Systems, Birla Institute of Technology and Science, Pilani-Hyderabad Campus, Secunderabad, India

    Raghunath Reddy Madireddy

  2. Department of Computer Science and Engineering, Indian Institute of Technology Ropar, Rupnagar, Punjab, India

    Apurva Mudgal

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  1. Raghunath Reddy Madireddy
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  2. Apurva Mudgal
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Correspondence to Raghunath Reddy Madireddy.

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A preliminary version of this paper appeared in the 18th International Workshop on Approximation and Online Algorithms WAOA 2020 [13].

Raghunath Reddy Madireddy: This research was done while the author was a graduate student at Indian Institute of Technology Ropar, Rupnagar, Punjab, India.

Apurva Mudgal: Partially supported by grant No. SB/FTP/ETA-434/2012 under DST-SERB Fast Track Scheme for Young Scientist, India.

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Madireddy, R.R., Mudgal, A. A Constant–Factor Approximation Algorithm for Red–Blue Set Cover with Unit Disks. Algorithmica 85, 100–132 (2023). https://doi.org/10.1007/s00453-022-01012-z

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  • DOI: https://doi.org/10.1007/s00453-022-01012-z

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