TY - GEN

T1 - Approximating minimum power covers of intersecting families and directed connectivity problems

AU - Nutov, Zeev

N1 - Copyright:
Copyright 2020 Elsevier B.V., All rights reserved.

PY - 2006

Y1 - 2006

N2 - Given a (directed) graph with costs on the edges, the power of a node is the maximum cost of an edge leaving it, and the power of the graph is the sum of the powers of its nodes. Motivated by applications for wireless networks, we consider fundamental directed connectivity network design problems under the power minimization criteria: the k-outconnected and the k-connected spanning subgraph problems. For k = 1 these problems are at least as hard as the Set-Cover problem and thus have an Ω(ln |V|) approximation threshold, while for arbitrary k a polylogarithmic approximation algorithm is unlikely. We give an O(ln |V|)-approximation algorithm for any constant k. In fact, our results are based on a much more general O(ln |V|)-approximation algorithm for the problem of finding a min-power edge-cover of an intersecting set-family; a set-family F on a groundset V is intersecting if X ∩ Y, X ∪ Y ∈ F for any intersecting X, Y ∈ F, and an edge set I covers F if for every X ∈ F there is an edge in I entering X.

AB - Given a (directed) graph with costs on the edges, the power of a node is the maximum cost of an edge leaving it, and the power of the graph is the sum of the powers of its nodes. Motivated by applications for wireless networks, we consider fundamental directed connectivity network design problems under the power minimization criteria: the k-outconnected and the k-connected spanning subgraph problems. For k = 1 these problems are at least as hard as the Set-Cover problem and thus have an Ω(ln |V|) approximation threshold, while for arbitrary k a polylogarithmic approximation algorithm is unlikely. We give an O(ln |V|)-approximation algorithm for any constant k. In fact, our results are based on a much more general O(ln |V|)-approximation algorithm for the problem of finding a min-power edge-cover of an intersecting set-family; a set-family F on a groundset V is intersecting if X ∩ Y, X ∪ Y ∈ F for any intersecting X, Y ∈ F, and an edge set I covers F if for every X ∈ F there is an edge in I entering X.

UR - http://www.scopus.com/inward/record.url?scp=33750060038&partnerID=8YFLogxK

U2 - 10.1007/11830924_23

DO - 10.1007/11830924_23

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AN - SCOPUS:33750060038

SN - 3540380442

SN - 9783540380443

T3 - Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)

SP - 236

EP - 247

BT - Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques - 9th International Workshop on Approximation Algorithms for Combinatorial Optimization Problems, APPROX 2006 a

PB - Springer Verlag

T2 - 9th International Workshop on Approximation Algorithms for Combinatorial Optimization Problems, APPROX 2006 and 10th International Workshop on Randomization and Computation, RANDOM 2006

Y2 - 28 August 2006 through 30 August 2006

ER -