research-article

Sdp gaps and ugc hardness for multiway cut, 0-extension, and metric labeling

Authors:

Rajsekar Manokaran,

Joseph (Seffi) Naor,

Prasad Raghavendra,

Roy SchwartzAuthors Info & Claims

STOC '08: Proceedings of the fortieth annual ACM symposium on Theory of computing

Pages 11 - 20

https://doi.org/10.1145/1374376.1374379

Published: 17 May 2008 Publication History

Abstract

The connection between integrality gaps and computational hardness of discrete optimization problems is an intriguing question. In recent years, this connection has prominently figured in several tight UGC-based hardness results. We show in this paper a direct way of turning integrality gaps into hardness results for several fundamental classification problems. Specifically, we convert linear programming integrality gaps for the Multiway Cut, 0-Extension, and and Metric Labeling problems into UGC-based hardness results. Qualitatively, our result suggests that if the unique games conjecture is true then a linear relaxation of the latter problems studied in several papers (so-called earthmover linear program) yields the best possible approximation. Taking this a step further, we also obtain integrality gaps for a semi-definite programming relaxation matching the integrality gaps of the earthmover linear program. Prior to this work, there was an intriguing possibility of obtaining better approximation factors for labeling problems via semi-definite programming.

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Cited By

Dalirrooyfard MMitrovic SNevmyvaka YOh ANaumann TGloberson ASaenko KHardt MLevine S(2023)Nearly tight bounds for differentially private multiway cutProceedings of the 37th International Conference on Neural Information Processing Systems10.5555/3666122.3667206(24947-24965)Online publication date: 10-Dec-2023
https://dl.acm.org/doi/10.5555/3666122.3667206
Ghoshal SLee E(2023)On Lifting Integrality Gaps to SSEH Hardness for Globally Constrained CSPs2023 IEEE 64th Annual Symposium on Foundations of Computer Science (FOCS)10.1109/FOCS57990.2023.00009(26-36)Online publication date: 6-Nov-2023
https://doi.org/10.1109/FOCS57990.2023.00009
Chandrasekaran KWang W(2022)$$\ell _p$$-Norm Multiway CutAlgorithmica10.1007/s00453-022-00983-384:9(2667-2701)Online publication date: 23-May-2022
https://doi.org/10.1007/s00453-022-00983-3
Show More Cited By

Index Terms

Sdp gaps and ugc hardness for multiway cut, 0-extension, and metric labeling
1. Theory of computation
  1. Randomness, geometry and discrete structures

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cover image ACM Conferences

STOC '08: Proceedings of the fortieth annual ACM symposium on Theory of computing

May 2008

712 pages

ISBN:9781605580470

DOI:10.1145/1374376

General Chair:
Richard Ladner
University of Washington
,
Program Chair:
Cynthia Dwork
Microsoft Research, Silicon Valley

Copyright © 2008 ACM.

Permission to make digital or hard copies of all or part of this work for personal or classroom use is granted without fee provided that copies are not made or distributed for profit or commercial advantage and that copies bear this notice and the full citation on the first page. Copyrights for components of this work owned by others than ACM must be honored. Abstracting with credit is permitted. To copy otherwise, or republish, to post on servers or to redistribute to lists, requires prior specific permission and/or a fee. Request permissions from [email protected]

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Published: 17 May 2008

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May 17 - 20, 2008

British Columbia, Victoria, Canada

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STOC '08 Paper Acceptance Rate 80 of 325 submissions, 25%;

Overall Acceptance Rate 1,469 of 4,586 submissions, 32%

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Cited By

Dalirrooyfard MMitrovic SNevmyvaka YOh ANaumann TGloberson ASaenko KHardt MLevine S(2023)Nearly tight bounds for differentially private multiway cutProceedings of the 37th International Conference on Neural Information Processing Systems10.5555/3666122.3667206(24947-24965)Online publication date: 10-Dec-2023
https://dl.acm.org/doi/10.5555/3666122.3667206
Ghoshal SLee E(2023)On Lifting Integrality Gaps to SSEH Hardness for Globally Constrained CSPs2023 IEEE 64th Annual Symposium on Foundations of Computer Science (FOCS)10.1109/FOCS57990.2023.00009(26-36)Online publication date: 6-Nov-2023
https://doi.org/10.1109/FOCS57990.2023.00009
Chandrasekaran KWang W(2022)$$\ell _p$$-Norm Multiway CutAlgorithmica10.1007/s00453-022-00983-384:9(2667-2701)Online publication date: 23-May-2022
https://doi.org/10.1007/s00453-022-00983-3
Schwartz RTur NKhuller SVassilevska Williams V(2021)The metric relaxation for 0-extension admits an Ω(logk) gapProceedings of the 53rd Annual ACM SIGACT Symposium on Theory of Computing10.1145/3406325.3451071(1601-1614)Online publication date: 15-Jun-2021
https://dl.acm.org/doi/10.1145/3406325.3451071
Chiu CHe T(2021)Stealthy DGoS Attack: DeGrading of Service Under the Watch of Network TomographyIEEE/ACM Transactions on Networking10.1109/TNET.2021.305823029:3(1294-1307)Online publication date: Jun-2021
https://doi.org/10.1109/TNET.2021.3058230
Shim SBandi CChopra S(2021)On the (near) optimality of extended formulations for multi-way cut in social networksOptimization and Engineering10.1007/s11081-021-09648-6Online publication date: 6-Jul-2021
https://doi.org/10.1007/s11081-021-09648-6
Velednitsky MHochbaum D(2020)Isolation branching: a branch and bound algorithm for the k-terminal cut problemJournal of Combinatorial Optimization10.1007/s10878-020-00534-y44:3(1659-1679)Online publication date: 7-Feb-2020
https://doi.org/10.1007/s10878-020-00534-y
Bérczi KChandrasekaran KKirály TMadan V(2020)Improving the integrality gap for multiway cutMathematical Programming10.1007/s10107-020-01485-2Online publication date: 6-Mar-2020
https://doi.org/10.1007/s10107-020-01485-2
Abrahamsen MGiannopoulos PLöffler MRote G(2020)Geometric Multicut: Shortest Fences for Separating Groups of Objects in the PlaneDiscrete & Computational Geometry10.1007/s00454-020-00232-w64:3(575-607)Online publication date: 1-Oct-2020
https://dl.acm.org/doi/10.1007/s00454-020-00232-w
Pansari PRussell CKumar M(2019)Linear programming-based submodular extensions for marginal estimationComputer Vision and Image Understanding10.1016/j.cviu.2019.102824(102824)Online publication date: Sep-2019
https://doi.org/10.1016/j.cviu.2019.102824
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