An analysis of graph cut size for transductive learning
ICML '06 Proceedings of the 23rd international conference on Machine learning
On a bidirected relaxation for the MULTIWAY CUT problem
Discrete Applied Mathematics - Special issue: Max-algebra
The multi-multiway cut problem
Theoretical Computer Science
On a bidirected relaxation for the MULTIWAY CUT problem
Discrete Applied Mathematics
Approximation algorithms for k-hurdle problems
LATIN'08 Proceedings of the 8th Latin American conference on Theoretical informatics
Strategic multiway cut and multicut games
WAOA'10 Proceedings of the 8th international conference on Approximation and online algorithms
Submodular cost allocation problem and applications
ICALP'11 Proceedings of the 38th international colloquim conference on Automata, languages and programming - Volume Part I
Approximation algorithms for graph homomorphism problems
APPROX'06/RANDOM'06 Proceedings of the 9th international conference on Approximation Algorithms for Combinatorial Optimization Problems, and 10th international conference on Randomization and Computation
An approximation algorithm for the Generalized k-Multicut problem
Discrete Applied Mathematics
Simplex partitioning via exponential clocks and the multiway cut problem
Proceedings of the forty-fifth annual ACM symposium on Theory of computing
On the generalized multiway cut in trees problem
Journal of Combinatorial Optimization
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Given an undirected graph with edge costs and a subset ofk=3 nodes calledterminals, a multiway, ork-way, cut is a subset of the edges whose removal disconnects each terminal from the others. The multiway cut problem is to find a minimum-cost multiway cut. This problem is Max-SNP hard. Recently, Calinescu et al. (Calinescu, G., H. Karloff, Y. Rabani. 2000. An improved approximation algorithm for Multiway Cut.J. Comput. System Sci.60(3) 564--574) gave a novel geometric relaxation of the problem and a rounding scheme that produced a (3/2-1/ k)-approximation algorithm.In this paper, we study their geometric relaxation. In particular, we study the worst-case ratio between the value of the relaxation and the value of the minimum multicut (the so-called integrality gap of the relaxation). Fork=3, we show the integrality gap is 12/11, giving tight upper and lower bounds. That is, we exhibit a family of graphs with integrality gaps arbitrarily close to 12/11 and give an algorithm that finds a cut of value 12/11 times the relaxation value. Our lower bound shows that this is the best possible performance guarantee for any algorithm based purely on the value of the relaxation. Our upper bound meets the lower bound and improves the factor of 7/6 shown by Calinescu et al.For allk, we show that there exists a rounding scheme with performance ratio equal to the integrality gap, and we give explicit constructions of polynomial-time rounding schemes that lead to improved upper bounds. Fork=4 and 5, our best upper bounds are based on computer-constructed rounding schemes (with computer proofs of correctness). For generalk we give an algorithm with performance ratio 1.3438-e k .Our results were discovered with the help of computational experiments that we also describe here.