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Combinatorial dominance guarantees for problems with infeasible solutions

Authors:

Steven S. Skiena,

Yochai TwittoAuthors Info & Claims

ACM Transactions on Algorithms (TALG), Volume 5, Issue 1

Article No.: 8, Pages 1 - 29

https://doi.org/10.1145/1435375.1435383

Published: 12 December 2008 Publication History

Abstract

The design and analysis of approximation algorithms for NP-hard problems is perhaps the most active research area in the theory of combinatorial algorithms. In this article, we study the notion of a combinatorial dominance guarantee as a way for assessing the performance of a given approximation algorithm. An f(n) dominance bound is a guarantee that the heuristic always returns a solution not worse than at least f(n) solutions. We give tight analysis of many heuristics, and establish novel and interesting dominance guarantees even for certain inapproximable problems and heuristic search algorithms. For example, we show that the maximal matching heuristic of VERTEX COVER offers a combinatorial dominance guarantee of 2ⁿ − (1.839 + o(1))ⁿ. We also give inapproximability results for most of the problems we discuss.

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Cited By

Gutin G(2024)Domination Analysis in Combinatorial OptimizationEncyclopedia of Optimization10.1007/978-3-030-54621-2_136-1(1-12)Online publication date: 8-May-2024
https://doi.org/10.1007/978-3-030-54621-2_136-1
Berend DSkiena STwitto Y(2018)Dominance Certificates for Combinatorial Optimization ProblemsOptimization Problems in Graph Theory10.1007/978-3-319-94830-0_6(107-122)Online publication date: 28-Sep-2018
https://doi.org/10.1007/978-3-319-94830-0_6
Punnen ASripratak PKarapetyan D(2015)Average value of solutions for the bipartite boolean quadratic programs and rounding algorithmsTheoretical Computer Science10.1016/j.tcs.2014.11.008565:C(77-89)Online publication date: 2-Feb-2015
https://dl.acm.org/doi/10.1016/j.tcs.2014.11.008
Show More Cited By

Index Terms

Combinatorial dominance guarantees for problems with infeasible solutions
1. Theory of computation
  1. Design and analysis of algorithms

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Published In

cover image ACM Transactions on Algorithms

ACM Transactions on Algorithms Volume 5, Issue 1

November 2008

281 pages

ISSN:1549-6325

EISSN:1549-6333

DOI:10.1145/1435375

Issue’s Table of Contents

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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Association for Computing Machinery

New York, NY, United States

Publication History

Published: 12 December 2008

Accepted: 01 September 2007

Revised: 01 August 2007

Received: 01 March 2006

Published in TALG Volume 5, Issue 1

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Cited By

Gutin G(2024)Domination Analysis in Combinatorial OptimizationEncyclopedia of Optimization10.1007/978-3-030-54621-2_136-1(1-12)Online publication date: 8-May-2024
https://doi.org/10.1007/978-3-030-54621-2_136-1
Berend DSkiena STwitto Y(2018)Dominance Certificates for Combinatorial Optimization ProblemsOptimization Problems in Graph Theory10.1007/978-3-319-94830-0_6(107-122)Online publication date: 28-Sep-2018
https://doi.org/10.1007/978-3-319-94830-0_6
Punnen ASripratak PKarapetyan D(2015)Average value of solutions for the bipartite boolean quadratic programs and rounding algorithmsTheoretical Computer Science10.1016/j.tcs.2014.11.008565:C(77-89)Online publication date: 2-Feb-2015
https://dl.acm.org/doi/10.1016/j.tcs.2014.11.008
Wang Y(2015)An approximate method to compute a sparse graph for traveling salesman problemExpert Systems with Applications: An International Journal10.1016/j.eswa.2015.02.03742:12(5150-5162)Online publication date: 15-Jul-2015
https://dl.acm.org/doi/10.1016/j.eswa.2015.02.037
Kühn DOsthus DPatel V(2015)A domination algorithm for {0,1}-instances of the travelling salesman problemRandom Structures & Algorithms10.1002/rsa.2060048:3(427-453)Online publication date: 8-Oct-2015
https://doi.org/10.1002/rsa.20600
Wang Y(2013)A Representation Model for TSP2013 IEEE 10th International Conference on High Performance Computing and Communications & 2013 IEEE International Conference on Embedded and Ubiquitous Computing10.1109/HPCC.and.EUC.2013.38(204-209)Online publication date: Nov-2013
https://doi.org/10.1109/HPCC.and.EUC.2013.38
Punnen ASripratak PKarapetyan D(2013)Domination analysis of algorithms for bipartite boolean quadratic programsProceedings of the 19th international conference on Fundamentals of Computation Theory10.1007/978-3-642-40164-0_26(271-282)Online publication date: 19-Aug-2013
https://dl.acm.org/doi/10.1007/978-3-642-40164-0_26
Twitto Y(2008)Dominance guarantees for above-average solutionsDiscrete Optimization10.1016/j.disopt.2007.11.0095:3(563-568)Online publication date: 1-Aug-2008
https://dl.acm.org/doi/10.1016/j.disopt.2007.11.009
Gutin GGoldengorin BHuang J(2008)Worst case analysis of Max-Regret, Greedy and other heuristics for Multidimensional Assignment and Traveling Salesman ProblemsJournal of Heuristics10.1007/s10732-007-9033-314:2(169-181)Online publication date: 1-Apr-2008
https://dl.acm.org/doi/10.1007/s10732-007-9033-3

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