TY - GEN

T1 - Approximation algorithms and hardness results for shortest path based graph orientations

AU - Blokh, Dima

AU - Segev, Danny

AU - Sharan, Roded

PY - 2012

Y1 - 2012

N2 - The graph orientation problem calls for orienting the edges of an undirected graph so as to maximize the number of pre-specified source-target vertex pairs that admit a directed path from the source to the target. Most algorithmic approaches to this problem share a common preprocessing step, in which the input graph is reduced to a tree by repeatedly contracting its cycles. While this reduction is valid from an algorithmic perspective, the assignment of directions to the edges of the contracted cycles becomes arbitrary, and the connecting source-target paths may be arbitrarily long. In the context of biological networks, the connection of vertex pairs via shortest paths is highly motivated, leading to the following variant: Given an undirected graph and a collection of source-target vertex pairs, assign directions to the edges so as to maximize the number of pairs that are connected by a shortest (in the original graph) directed path. Here we study this variant, provide strong inapproximability results for it and propose an approximation algorithm for the problem, as well as for relaxations of it where the connecting paths need only be approximately shortest.

AB - The graph orientation problem calls for orienting the edges of an undirected graph so as to maximize the number of pre-specified source-target vertex pairs that admit a directed path from the source to the target. Most algorithmic approaches to this problem share a common preprocessing step, in which the input graph is reduced to a tree by repeatedly contracting its cycles. While this reduction is valid from an algorithmic perspective, the assignment of directions to the edges of the contracted cycles becomes arbitrary, and the connecting source-target paths may be arbitrarily long. In the context of biological networks, the connection of vertex pairs via shortest paths is highly motivated, leading to the following variant: Given an undirected graph and a collection of source-target vertex pairs, assign directions to the edges so as to maximize the number of pairs that are connected by a shortest (in the original graph) directed path. Here we study this variant, provide strong inapproximability results for it and propose an approximation algorithm for the problem, as well as for relaxations of it where the connecting paths need only be approximately shortest.

UR - http://www.scopus.com/inward/record.url?scp=84863088040&partnerID=8YFLogxK

U2 - 10.1007/978-3-642-31265-6_6

DO - 10.1007/978-3-642-31265-6_6

M3 - Conference contribution

AN - SCOPUS:84863088040

SN - 9783642312649

T3 - Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)

SP - 70

EP - 82

BT - Combinatorial Pattern Matching - 23rd Annual Symposium, CPM 2012, Proceedings

T2 - 23rd Annual Symposium on Combinatorial Pattern Matching, CPM 2012

Y2 - 3 July 2012 through 5 July 2012

ER -