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.
Bibliographical noteFunding Information:
Acknowledgments. M.E. was supported by a research grant from the Dr. Alexander und Rita Besser-Stiftung. R.S. was supported by a research grant from the Israel Science Foundation (grant no. 385/06). U.Z. was supported by BSF grant no. 2006261. We thank Rani Hod for his help with the proof of Lemma 3.4.
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ASJC Scopus subject areas
- Modeling and Simulation
- Computational Mathematics
- Applied Mathematics