Approximation algorithms for orienting mixed graphs

Authors:
Michael Elberfeld;Danny Segev;Colin R. Davidson;Dana Silverbush;Roded Sharan
Affiliations:
Institute of Theoretical Computer Science, University of Lübeck, 23538 Lübeck, Germany;Department of Statistics, University of Haifa, Haifa 31905, Israel;Faculty of Mathematics, University of Waterloo, Waterloo, Canada, N2L 3G1;Blavatnik School of Computer Science, Tel Aviv University, Tel Aviv 69978, Israel;Blavatnik School of Computer Science, Tel Aviv University, Tel Aviv 69978, Israel
Venue:
Theoretical Computer Science
Year:
2013

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Abstract

Graph orientation is a fundamental problem in graph theory that has recently arisen in the study of signaling-regulatory pathways in protein networks. Given a graph and a list of source-target vertex pairs, one wishes to assign directions to the edges so as to maximize the number of pairs that admit a directed source-to-target path. When the input graph is undirected, a sub-logarithmic approximation is known for this problem. However, the approximability of the biologically-relevant variant, in which the input graph has both directed and undirected edges, was left open. Here we give the first approximation algorithms to this problem. Our algorithms provide a sub-linear guarantee in the general case, and logarithmic guarantees for structured instances.