On the Approximability of Reachability-Preserving Network Orientations

Michael Elberfeld, Vineet Bafna, Iftah Gamzu, Alexander Medvedovsky, Danny Segev, Dana Silverbush, Uri Zwick, Roded Sharan
<span title="2011-11-28">2011</span> <i title="Internet Mathematics"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/btilruk4pjav5n4cm5wszidqtm" style="color: black;">Internet Mathematics</a> </i> &nbsp;
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
more &raquo; ... actor 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.
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1080/15427951.2011.604554">doi:10.1080/15427951.2011.604554</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/msvkismcd5er7kxxlgrq4div7y">fatcat:msvkismcd5er7kxxlgrq4div7y</a> </span>
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