TY - GEN

T1 - Simplex transformations and the multiway cut problem

AU - Buchbinder, Niv

AU - Schwartz, Roy

AU - Weizman, Baruch

N1 - Publisher Copyright:
Copyright © by SIAM.

PY - 2017

Y1 - 2017

N2 - We consider Multiway Cut, a basic graph partitioning problem in which the goal is to find the minimum weight collection of edges disconnecting a given set of special vertices called terminals. Multiway Cut admits a well known simplex embedding relaxation, where rounding this embedding is equivalent to partitioning the simplex. Current best known solutions to the problem are comprised of a mix of several different ingredients, resulting in intricate algorithms. Moreover, the best of these algorithms is too complex to fully analyze analytically and its approximation factor was verified using a computer. We propose a new approach to simplex partitioning and the Multiway Cut problem based on general transformations of the simplex that allow dependencies between the different variables. Our approach admits much simpler algorithms, and in addition yields an approximation guarantee for the Multiway Cut problem that (roughly) matches the current best computer verified approximation factor.

AB - We consider Multiway Cut, a basic graph partitioning problem in which the goal is to find the minimum weight collection of edges disconnecting a given set of special vertices called terminals. Multiway Cut admits a well known simplex embedding relaxation, where rounding this embedding is equivalent to partitioning the simplex. Current best known solutions to the problem are comprised of a mix of several different ingredients, resulting in intricate algorithms. Moreover, the best of these algorithms is too complex to fully analyze analytically and its approximation factor was verified using a computer. We propose a new approach to simplex partitioning and the Multiway Cut problem based on general transformations of the simplex that allow dependencies between the different variables. Our approach admits much simpler algorithms, and in addition yields an approximation guarantee for the Multiway Cut problem that (roughly) matches the current best computer verified approximation factor.

UR - http://www.scopus.com/inward/record.url?scp=85016223698&partnerID=8YFLogxK

U2 - 10.1137/1.9781611974782.158

DO - 10.1137/1.9781611974782.158

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AN - SCOPUS:85016223698

T3 - Proceedings of the Annual ACM-SIAM Symposium on Discrete Algorithms

SP - 2400

EP - 2410

BT - 28th Annual ACM-SIAM Symposium on Discrete Algorithms, SODA 2017

A2 - Klein, Philip N.

PB - Association for Computing Machinery

T2 - 28th Annual ACM-SIAM Symposium on Discrete Algorithms, SODA 2017

Y2 - 16 January 2017 through 19 January 2017

ER -