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.
Bibliographical noteFunding Information:
M.E. was supported by a research grant from the Dr. Alexander und Rita Besser-Stiftung. C.R.D. would like to thank Gerry Schwartz, Heather Reisman, and the University of Waterloo-Haifa International Experience Program for funding his visit to the University of Haifa, during which part of this work was done. R.S. was supported by a research grant from the Israel Science Foundation (grant no. 241/11).
- Approximation algorithm
- Graph orientation
- Mixed graph
- Protein-protein interaction network
ASJC Scopus subject areas
- Theoretical Computer Science
- Computer Science (all)