A Graph-Theoretic Game and its Application to the $k$-Server Problem
SIAM Journal on Computing
Clique is hard to approximate within n1-
FOCS '96 Proceedings of the 37th Annual Symposium on Foundations of Computer Science
SIAM Journal on Computing
WABI '08 Proceedings of the 8th international workshop on Algorithms in Bioinformatics
Nearly Tight Low Stretch Spanning Trees
FOCS '08 Proceedings of the 2008 49th Annual IEEE Symposium on Foundations of Computer Science
Improved orientations of physical networks
WABI'10 Proceedings of the 10th international conference on Algorithms in bioinformatics
Optimally orienting physical networks
RECOMB'11 Proceedings of the 15th Annual international conference on Research in computational molecular biology
Approximation algorithms for orienting mixed graphs
CPM'11 Proceedings of the 22nd annual conference on Combinatorial pattern matching
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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.