Internet Mathematics

On the Approximability of Reachability-Preserving Network Orientations

Michael Elberfeld, Vineet Bafna, Iftah Gamzu, Alexander Medvedovsky, Danny Segev, Dana Silverbush, Uri Zwick, and Roded Sharan

Full-text: Open access


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.

Article information

Internet Math., Volume 7, Number 4 (2011), 209-232.

First available in Project Euclid: 8 December 2011

Permanent link to this document

Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier


Elberfeld, Michael; Bafna, Vineet; Gamzu, Iftah; Medvedovsky, Alexander; Segev, Danny; Silverbush, Dana; Zwick, Uri; Sharan, Roded. On the Approximability of Reachability-Preserving Network Orientations. Internet Math. 7 (2011), no. 4, 209--232.

Export citation