On the approximability of reachability-preserving network orientations

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

Research output: Contribution to journalArticlepeer-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 languageEnglish
Pages (from-to)209-232
Number of pages24
JournalInternet Mathematics
Volume7
Issue number4
DOIs
StatePublished - 1 Jan 2011

Funding

FundersFunder number
Dr. Alexander und Rita Besser-Stiftung
United States-Israel Binational Science Foundation2006261
Israel Science Foundation385/06

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