Approximation algorithms for Steiner and directed multicuts
Journal of Algorithms
Divide-and-conquer approximation algorithms via spreading metrics
Journal of the ACM (JACM)
Approximating Fractional Multicommodity Flow Independent of the Number of Commodities
SIAM Journal on Discrete Mathematics
Introduction to Algorithms
Approximate Max-Flow Min-(Multi)Cut Theorems and Their Applications
SIAM Journal on Computing
Improved results for directed multicut
SODA '03 Proceedings of the fourteenth annual ACM-SIAM symposium on Discrete algorithms
Graph decomposition and a greedy algorithm for edge-disjoint paths
SODA '04 Proceedings of the fifteenth annual ACM-SIAM symposium on Discrete algorithms
Approximating Directed Multicuts
Combinatorica
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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 every (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 min${\{O({\sqrt n}), opt\}}$ by Anupam Gupta [5], where n = |V|, and opt is the optimal solution value. All known non-trivial approximation algorithms for the problem solve large linear programs. We give the first combinatorial approximation algorithms for the problem. Our main result is a $\tilde O (n^{2/3}/opt^{1/3})$-approximation algorithm for UDM, which improves the ${\sqrt n}$-approximation for opt = ${\it \Omega}({\it n}^{\rm 1/2 + {\it \epsilon}}$). Combined with the paper of Gupta [5], 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.