The Complexity of Multiterminal Cuts
SIAM Journal on Computing
Cut problems and their application to divide-and-conquer
Approximation algorithms for NP-hard problems
An improved approximation algorithm for multiway cut
STOC '98 Proceedings of the thirtieth annual ACM symposium on Theory of computing
Multicommodity max-flow min-cut theorems and their use in designing approximation algorithms
Journal of the ACM (JACM)
On the power of unique 2-prover 1-round games
STOC '02 Proceedings of the thiry-fourth annual ACM symposium on Theory of computing
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
Cutting and Partitioning a Graph aifter a Fixed Pattern (Extended Abstract)
Proceedings of the 10th Colloquium on Automata, Languages and Programming
Clustering with Qualitative Information
FOCS '03 Proceedings of the 44th Annual IEEE Symposium on Foundations of Computer Science
Rounding Algorithms for a Geometric Embedding of Minimum Multiway Cut
Mathematics of Operations Research
O(√log n) approximation algorithms for min UnCut, min 2CNF deletion, and directed cut problems
Proceedings of the thirty-seventh annual ACM symposium on Theory of computing
Approximating Directed Multicuts
Combinatorica
On the Hardness of Approximating Multicut and Sparsest-Cut
CCC '05 Proceedings of the 20th Annual IEEE Conference on Computational Complexity
Approximation algorithms for requirement cut on graphs
APPROX'05/RANDOM'05 Proceedings of the 8th international workshop on Approximation, Randomization and Combinatorial Optimization Problems, and Proceedings of the 9th international conference on Randamization and Computation: algorithms and techniques
Improved fixed-parameter algorithms for two feedback set problems
WADS'05 Proceedings of the 9th international conference on Algorithms and Data Structures
Untangling the cross-lingual link structure of Wikipedia
ACL '10 Proceedings of the 48th Annual Meeting of the Association for Computational Linguistics
Separator-based data reduction for signed graph balancing
Journal of Combinatorial Optimization
Compression via matroids: a randomized polynomial kernel for odd cycle transversal
Proceedings of the twenty-third annual ACM-SIAM symposium on Discrete Algorithms
An improved approximation algorithm for requirement cut
Operations Research Letters
Partitioning into colorful components by minimum edge deletions
CPM'12 Proceedings of the 23rd Annual conference on Combinatorial Pattern Matching
| Hi-index | 5.23 |
In this paper, we define and study a natural generalization of the multicut and multiway cut problems: the minimum multi-multiway cut problem. The input to the problem is a weighted undirected graph G=(V,E) and k sets S"1,S"2,...,S"k of vertices. The goal is to find a subset of edges of minimum total weight whose removal completely disconnects each one of the sets S"1,S"2,...,S"k, i.e., disconnects every pair of vertices u and v such that u,v@?S"i, for some i. This problem generalizes both the multicut problem, when |S"i|=2, for 1@?i@?k, and the multiway cut problem, when k=1. We present an approximation algorithm for the multi-multiway cut problem with an approximation ratio which matches that obtained by Garg, Vazirani, and Yannakakis on the standard multicut problem. Namely, our algorithm has an O(logk) approximation ratio. Moreover, we consider instances of the minimum multi-multiway cut problem which are known to have an optimal solution of light weight. We show that our algorithm has an approximation ratio substantially better than O(logk) when restricted to such ''light'' instances. Specifically, we obtain an O(logLP)-approximation algorithm for the problem when all edge weights are at least 1 (here LP denotes the value of a natural linear programming relaxation of the problem). The latter improves the O(logLPloglogLP) approximation ratio for the minimum multicut problem (implied by the work of Seymour and Even et al.).