Article

Polylogarithmic inapproximability

Authors:

Robert KrauthgamerAuthors Info & Claims

STOC '03: Proceedings of the thirty-fifth annual ACM symposium on Theory of computing

Pages 585 - 594

https://doi.org/10.1145/780542.780628

Published: 09 June 2003 Publication History

Abstract

We provide the first hardness result of a polylogarithmic approximation ratio for a natural NP-hard optimization problem. We show that for every fixed ε>0, the GROUP-STEINER-TREE problem admits no efficient log^2-ε k approximation, where k denotes the number of groups (or, alternatively, the input size), unless NP has quasi polynomial Las-Vegas algorithms. This hardness result holds even for input graphs which are Hierarchically Well-Separated Trees, introduced by Bartal [FOCS, 1996]. For these trees (and also for general trees), our bound is nearly tight with the log-squared approximation currently known. Our results imply that for every fixed ε>0, the DIRECTED-STEINER TREE problem admits no log^2-ε n--approximation, where n is the number of vertices in the graph, under the same complexity assumption.

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https://dl.acm.org/doi/10.1145/3632623
Wang XCheng GChua TNgo CKa-Wei Lee RKumar RLauw H(2024)A Fast Hop-Biased Approximation Algorithm for the Quadratic Group Steiner Tree ProblemProceedings of the ACM Web Conference 202410.1145/3589334.3645325(312-321)Online publication date: 13-May-2024
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Index Terms

Polylogarithmic inapproximability
1. Theory of computation
  1. Design and analysis of algorithms

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Published In

cover image ACM Conferences

STOC '03: Proceedings of the thirty-fifth annual ACM symposium on Theory of computing

June 2003

740 pages

ISBN:1581136749

DOI:10.1145/780542

Conference Chair:
Lawrence L. Larmore
University of Nevada Las Vegas, Las Vegas, NV
,
Program Chair:
Michel X. Goemans
Massachusetts Institute of Technology, Cambridge, MA

Copyright © 2003 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: 09 June 2003

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STOC03: The 35th Annual ACM Symposium on Theory of Computing

June 9 - 11, 2003

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STOC '03 Paper Acceptance Rate 80 of 270 submissions, 30%;

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

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https://dl.acm.org/doi/10.1145/3632623
Wang XCheng GChua TNgo CKa-Wei Lee RKumar RLauw H(2024)A Fast Hop-Biased Approximation Algorithm for the Quadratic Group Steiner Tree ProblemProceedings of the ACM Web Conference 202410.1145/3589334.3645325(312-321)Online publication date: 13-May-2024
https://dl.acm.org/doi/10.1145/3589334.3645325
Zhong YHuang WAdhikari B(2024)End-to-End Risk-Aware Reinforcement Learning to Detect Asymptomatic Cases in Healthcare Facilities2024 IEEE 12th International Conference on Healthcare Informatics (ICHI)10.1109/ICHI61247.2024.00019(83-92)Online publication date: 3-Jun-2024
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Nutov Z(2024)On Rooted k-Connectivity Problems in Quasi-Bipartite DigraphsOperations Research Forum10.1007/s43069-023-00285-65:1Online publication date: 17-Jan-2024
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Zhang KWang XCheng G(2023)Efficient Approximation Algorithms for the Diameter-Bounded Max-Coverage Group Steiner Tree ProblemProceedings of the ACM Web Conference 202310.1145/3543507.3583257(199-209)Online publication date: 30-Apr-2023
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