TY - JOUR

T1 - Approximation algorithm for Directed Multicuts

AU - Kortsarts, Yana

AU - Kortsarz, Guy

AU - Nutov, Zeev

N1 - Copyright:
Copyright 2020 Elsevier B.V., All rights reserved.

PY - 2005

Y1 - 2005

N2 - 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(√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 Ō(n2/3/opt1/3)- approximation algorithm for UDM, which improves the √n-approximation for opt = Ω(n1/2+ε). Combined with the paper of Gupta [5], we get that UDM can be approximated within better than O(√n), unless opt = Θ̃(√n). We also give a simple and fast O(n2/3)- approximation algorithm for DM.

AB - 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(√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 Ō(n2/3/opt1/3)- approximation algorithm for UDM, which improves the √n-approximation for opt = Ω(n1/2+ε). Combined with the paper of Gupta [5], we get that UDM can be approximated within better than O(√n), unless opt = Θ̃(√n). We also give a simple and fast O(n2/3)- approximation algorithm for DM.

UR - http://www.scopus.com/inward/record.url?scp=23944442827&partnerID=8YFLogxK

U2 - 10.1007/978-3-540-31833-0_7

DO - 10.1007/978-3-540-31833-0_7

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AN - SCOPUS:23944442827

SN - 0302-9743

VL - 3351

SP - 61

EP - 67

JO - Lecture Notes in Computer Science

JF - Lecture Notes in Computer Science

T2 - Second International Workshop on Approximation and Online Algorithms, WAOA 2004

Y2 - 14 September 2004 through 16 September 2004

ER -