On the approximability of reachability-preserving network orientations

Michael Elberfeld; Vineet Bafna; Iftah Gamzu; Alexander Medvedovsky; Danny Segev; Dana Silverbush; Uri Zwick; Roded Sharan

doi:10.1080/15427951.2011.604554

On the approximability of reachability-preserving network orientations

Michael Elberfeld, Vineet Bafna, Iftah Gamzu, Alexander Medvedovsky, Danny Segev, Dana Silverbush, Uri Zwick, Roded Sharan

Department of Statistics

Research output: Contribution to journal › Article › peer-review

Abstract

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.

Original language	English
Pages (from-to)	209-232
Number of pages	24
Journal	Internet Mathematics
Volume	7
Issue number	4
DOIs	https://doi.org/10.1080/15427951.2011.604554
State	Published - 1 Jan 2011

Bibliographical note

Funding Information:
Acknowledgments. M.E. was supported by a research grant from the Dr. Alexander und Rita Besser-Stiftung. R.S. was supported by a research grant from the Israel Science Foundation (grant no. 385/06). U.Z. was supported by BSF grant no. 2006261. We thank Rani Hod for his help with the proof of Lemma 3.4.

Publisher Copyright:
© Taylor & Francis Group, LLC.

ASJC Scopus subject areas

Modeling and Simulation
Computational Mathematics
Applied Mathematics

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10.1080/15427951.2011.604554

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title = "On the approximability of reachability-preserving network orientations",

abstract = "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.",

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AU - Silverbush, Dana

AU - Zwick, Uri

AU - Sharan, Roded

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On the approximability of reachability-preserving network orientations

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Bibliographical note

ASJC Scopus subject areas

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