TY - JOUR

T1 - Improved approximation algorithms for minimum power covering problems

AU - Calinescu, Gruia

AU - Kortsarz, Guy

AU - Nutov, Zeev

N1 - Publisher Copyright:
© 2019 Elsevier B.V.

PY - 2019/11/26

Y1 - 2019/11/26

N2 - 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.

AB - 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.

KW - Approximation algorithms

KW - Edge-cover

KW - Iterative randomized rounding

KW - Minimum power

KW - Terminal backup

UR - http://www.scopus.com/inward/record.url?scp=85068835496&partnerID=8YFLogxK

U2 - 10.1016/j.tcs.2019.07.010

DO - 10.1016/j.tcs.2019.07.010

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AN - SCOPUS:85068835496

SN - 0304-3975

VL - 795

SP - 285

EP - 300

JO - Theoretical Computer Science

JF - Theoretical Computer Science

ER -