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, Lübeck, Germany;Department of Statistics, University of Haifa, Haifa, Israel;Faculty of Mathematics, University of Waterloo, Waterloo, Canada;Blavatnik School of Computer Science, Tel Aviv University, Tel Aviv, Israel;Blavatnik School of Computer Science, Tel Aviv University, Tel Aviv, Israel
Venue:
CPM'11 Proceedings of the 22nd annual conference on Combinatorial pattern matching
Year:
2011

Citing 12
Cited 3

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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 ordered source-target vertex pairs, it calls for assigning directions to the edges of the graph 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 the 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 algorithm to this problem. Our algorithm provides a sub-linear guarantee in the general case, and logarithmic guarantees for structured instances.