An O(√n)-approximation algorithm for directed sparsest cut
Information Processing Letters
Improved approximation for directed cut problems
Proceedings of the thirty-ninth annual ACM symposium on Theory of computing
Polynomial flow-cut gaps and hardness of directed cut problems
Journal of the ACM (JACM)
An O(n)-approximation algorithm for directed sparsest cut
Information Processing Letters
APPROX/RANDOM'10 Proceedings of the 13th international conference on Approximation, and 14 the International conference on Randomization, and combinatorial optimization: algorithms and techniques
Theoretical Computer Science
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The Directed Multicut (DM) problem is: given a simple directed graph G = (V, E) with positive capacities ue on the edges, and a set K ⊆ V × V of ordered pairs of nodes of G, find a minimum capacity K-multicut; C ⊆ E is a K-multicut if in G - C there is no (s, t)-path for any (s, t) ⫅ K. In the uncapacitated case (UDM) the goal is to find a minimum size K-multicut. The best approximation ratio known for DM is $O(\min\{\sqrt{n},opt\})$ by Gupta, where n = |V|, and opt is the optimal solution value. All known nontrivial approximation algorithms for the problem solve large linear programs. We give the first combinatorial approximation algorithms for the problem. Our main result is an Õ(n2/3/opt1/3)-approximation algorithm for UDM, which improves the $O(\min\{opt,\sqrt{n}\})$-approximation for opt = Ω(n1/2+ε). Combined with the article of Gupta, we get that UDM can be approximated within better than $O(\sqrt n)$, unless $opt={\tilde \Theta}(\sqrt n)$. We also give a simple and fast O(n2/3)-approximation algorithm for DM. © 2005 Wiley Periodicals, Inc. NETWORKS, Vol. 45(4), 214–217 2005