Improved approximation algorithms for minimum power covering problems

Gruia Calinescu; Guy Kortsarz; Zeev Nutov

doi:10.1007/978-3-030-04693-4_9

Improved approximation algorithms for minimum power covering problems

Gruia Calinescu, Guy Kortsarz, Zeev Nutov

Computer Science discipline

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › peer-review

Abstract

Given an undirected graph with edge costs, the power of a node is the maximum cost of an edge incident to it, and the power of a graph is the sum of the powers of its nodes. Motivated by applications in wireless networks, we consider two network design problems under the power minimization criteria. In both problems we are given a graph G=(V,E) with edge costs and a set T⊆V of terminals. The goal is to find a minimum power edge subset F⊆E such that the graph H=(V,F) satisfies some prescribed requirements. In the Min-Power Edge-Cover problem, H should contain an edge incident to every terminal. Using the Iterative Randomized Rounding (IRR) method, we give an algorithm with expected approximation ratio 1.41; the ratio is reduced to 73/60 < 1.217 when T is an independent set in G. In the case of unit costs we also achieve ratio 73/60, and in addition give a simple efficient combinatorial algorithm with ratio 5/ 4. For all these NP-hard problems the previous best known ratio was 3/ 2. In the related Min-Power Terminal Backup problem, H should contain a path from every t∈T to some node in T\{t}. We obtain ratio 3/ 2 for this NP-hard problem, improving the trivial ratio of 2.

Original language	English
Title of host publication	Approximation and Online Algorithms - 16th International Workshop, WAOA 2018, Revised Selected Papers
Editors	Leah Epstein, Thomas Erlebach
Publisher	Springer Verlag
Pages	134-148
Number of pages	15
ISBN (Print)	9783030046927
DOIs	https://doi.org/10.1007/978-3-030-04693-4_9
State	Published - 2018
Event	16th Workshop on Approximation and Online Algorithms, WAOA 2018 - Helsinki, Finland Duration: 23 Aug 2018 → 24 Aug 2018

Publication series

Name	Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume	11312 LNCS
ISSN (Print)	0302-9743
ISSN (Electronic)	1611-3349

Conference

Conference	16th Workshop on Approximation and Online Algorithms, WAOA 2018
Country/Territory	Finland
City	Helsinki
Period	23/08/18 → 24/08/18

Bibliographical note

Funding Information:
Partially supported by NSF grant number 1540547. Gruia and Zeev thank Neil Olver for many useful discussions. Also, Gruia and Zeev acknowledge the support of the Hausdorff Trimester Program for Combinatorial Optimization (held at the Hausdorff Research Institute for Mathematics, University of Bonn).

Funding Information:
Partially supported by NSF grant number 1540547.

Funding Information:
Acknowledgment. Gruia and Zeev thank Neil Olver for many useful discussions. Also, Gruia and Zeev acknowledge the support of the Hausdorff Trimester Program for Combinatorial Optimization (held at the Hausdorff Research Institute for Mathematics, University of Bonn).

Publisher Copyright:
© Springer Nature Switzerland AG 2018.

Keywords

Approximation algorithms
Edge-cover
Iterative randomized rounding
Minimum power
Terminal backup

Access to Document

10.1007/978-3-030-04693-4_9

Cite this

Calinescu, G., Kortsarz, G., & Nutov, Z. (2018). Improved approximation algorithms for minimum power covering problems. In L. Epstein, & T. Erlebach (Eds.), Approximation and Online Algorithms - 16th International Workshop, WAOA 2018, Revised Selected Papers (pp. 134-148). (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 11312 LNCS). Springer Verlag. https://doi.org/10.1007/978-3-030-04693-4_9

Calinescu, Gruia ; Kortsarz, Guy ; Nutov, Zeev. / Improved approximation algorithms for minimum power covering problems. Approximation and Online Algorithms - 16th International Workshop, WAOA 2018, Revised Selected Papers. editor / Leah Epstein ; Thomas Erlebach. Springer Verlag, 2018. pp. 134-148 (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)).

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Calinescu, G, Kortsarz, G & Nutov, Z 2018, Improved approximation algorithms for minimum power covering problems. in L Epstein & T Erlebach (eds), Approximation and Online Algorithms - 16th International Workshop, WAOA 2018, Revised Selected Papers. Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics), vol. 11312 LNCS, Springer Verlag, pp. 134-148, 16th Workshop on Approximation and Online Algorithms, WAOA 2018, Helsinki, Finland, 23/08/18. https://doi.org/10.1007/978-3-030-04693-4_9

Improved approximation algorithms for minimum power covering problems. / Calinescu, Gruia; Kortsarz, Guy; Nutov, Zeev.
Approximation and Online Algorithms - 16th International Workshop, WAOA 2018, Revised Selected Papers. ed. / Leah Epstein; Thomas Erlebach. Springer Verlag, 2018. p. 134-148 (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 11312 LNCS).

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › peer-review

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Calinescu G, Kortsarz G, Nutov Z. Improved approximation algorithms for minimum power covering problems. In Epstein L, Erlebach T, editors, Approximation and Online Algorithms - 16th International Workshop, WAOA 2018, Revised Selected Papers. Springer Verlag. 2018. p. 134-148. (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)). doi: 10.1007/978-3-030-04693-4_9

Improved approximation algorithms for minimum power covering problems

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