TY - JOUR

T1 - On the approximability of reachability-preserving network orientations

AU - Elberfeld, Michael

AU - Bafna, Vineet

AU - Gamzu, Iftah

AU - Medvedovsky, Alexander

AU - Segev, Danny

AU - Silverbush, Dana

AU - Zwick, Uri

AU - Sharan, Roded

N1 - Publisher Copyright:
© Taylor & Francis Group, LLC.

PY - 2011/1/1

Y1 - 2011/1/1

N2 - We introduce a graph-orientation problem arising in the study of biological networks. Given an undirected graph and a list of ordered source–target vertex pairs, the goal is to orient the graph such that a maximum number of pairs admit a directed source-to-target path. We study the complexity and approximability of this problem. We show that the problem is NP-hard even on star graphs and hard to approximate to within some constant factor. On the positive side, we provide an Ω(log log n/ log n) factor approximation algorithm for the problem on n-vertex graphs. We further show that for any instance of the problem there exists an orientation of the input graph that satisfies a logarithmic fraction of all pairs and that this bound is tight up to a constant factor. Our techniques also lead to constant-factor approximation algorithms for some restricted variants of the problem.

AB - We introduce a graph-orientation problem arising in the study of biological networks. Given an undirected graph and a list of ordered source–target vertex pairs, the goal is to orient the graph such that a maximum number of pairs admit a directed source-to-target path. We study the complexity and approximability of this problem. We show that the problem is NP-hard even on star graphs and hard to approximate to within some constant factor. On the positive side, we provide an Ω(log log n/ log n) factor approximation algorithm for the problem on n-vertex graphs. We further show that for any instance of the problem there exists an orientation of the input graph that satisfies a logarithmic fraction of all pairs and that this bound is tight up to a constant factor. Our techniques also lead to constant-factor approximation algorithms for some restricted variants of the problem.

UR - http://www.scopus.com/inward/record.url?scp=84864072867&partnerID=8YFLogxK

U2 - 10.1080/15427951.2011.604554

DO - 10.1080/15427951.2011.604554

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AN - SCOPUS:84864072867

SN - 1542-7951

VL - 7

SP - 209

EP - 232

JO - Internet Mathematics

JF - Internet Mathematics

IS - 4

ER -