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Pipage Rounding: A New Method of Constructing Algorithms with Proven Performance Guarantee

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  • A.A. Ageev

    (Sobolev Institute of Mathematics)

  • M.I. Sviridenko

    (IBM T.J. Watson Research Center, P.O. Box)

Abstract

The paper presents a general method of designing constant-factor approximation algorithms for some discrete optimization problems with assignment-type constraints. The core of the method is a simple deterministic procedure of rounding of linear relaxations (referred to as pipage rounding). With the help of the method we design approximation algorithms with better performance guarantees for some well-known problems including MAXIMUM COVERAGE, MAX CUT with given sizes of parts and some of their generalizations.

Suggested Citation

  • A.A. Ageev & M.I. Sviridenko, 2004. "Pipage Rounding: A New Method of Constructing Algorithms with Proven Performance Guarantee," Journal of Combinatorial Optimization, Springer, vol. 8(3), pages 307-328, September.
    • Handle: RePEc:spr:jcomop:v:8:y:2004:i:3:d:10.1023_b:joco.0000038913.96607.c2
    DOI: 10.1023/B:JOCO.0000038913.96607.c2
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    Cited by:

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    8. Paul Gölz & Dominik Peters & Ariel Procaccia, 2022. "In This Apportionment Lottery, the House Always Wins," Post-Print hal-03834513, HAL.
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    14. Suning Gong & Qingqin Nong & Wenjing Liu & Qizhi Fang, 2019. "Parametric monotone function maximization with matroid constraints," Journal of Global Optimization, Springer, vol. 75(3), pages 833-849, November.
    15. Refael Hassin & R. Ravi & F. Sibel Salman, 2017. "Multiple facility location on a network with linear reliability order of edges," Journal of Combinatorial Optimization, Springer, vol. 34(3), pages 931-955, October.
    16. Haydar Evren & Manshu Khanna, 2021. "Affirmative Action's Cumulative Fractional Assignments," Papers 2111.11963, arXiv.org, revised Feb 2024.
    17. Suning Gong & Qingqin Nong & Shuyu Bao & Qizhi Fang & Ding-Zhu Du, 2023. "A fast and deterministic algorithm for Knapsack-constrained monotone DR-submodular maximization over an integer lattice," Journal of Global Optimization, Springer, vol. 85(1), pages 15-38, January.
    18. Marek Adamczyk & Maxim Sviridenko & Justin Ward, 2016. "Submodular Stochastic Probing on Matroids," Mathematics of Operations Research, INFORMS, vol. 41(3), pages 1022-1038, August.
    19. Simon Bruggmann & Rico Zenklusen, 2019. "Submodular Maximization Through the Lens of Linear Programming," Management Science, INFORMS, vol. 44(4), pages 1221-1244, November.
    20. Zengfu Wang & Bill Moran & Xuezhi Wang & Quan Pan, 2015. "An accelerated continuous greedy algorithm for maximizing strong submodular functions," Journal of Combinatorial Optimization, Springer, vol. 30(4), pages 1107-1124, November.
    21. Alfredo Torrico & Mohit Singh & Sebastian Pokutta & Nika Haghtalab & Joseph (Seffi) Naor & Nima Anari, 2021. "Structured Robust Submodular Maximization: Offline and Online Algorithms," INFORMS Journal on Computing, INFORMS, vol. 33(4), pages 1590-1607, October.
    22. Ariel Kulik & Hadas Shachnai & Tami Tamir, 2013. "Approximations for Monotone and Nonmonotone Submodular Maximization with Knapsack Constraints," Mathematics of Operations Research, INFORMS, vol. 38(4), pages 729-739, November.
    23. Zengfu Wang & Bill Moran & Xuezhi Wang & Quan Pan, 2016. "Approximation for maximizing monotone non-decreasing set functions with a greedy method," Journal of Combinatorial Optimization, Springer, vol. 31(1), pages 29-43, January.
    24. Refael Hassin & Jérôme Monnot & Danny Segev, 2007. "Approximation algorithms and hardness results for labeled connectivity problems," Journal of Combinatorial Optimization, Springer, vol. 14(4), pages 437-453, November.
    25. Jason R. Marden & Adam Wierman, 2013. "Distributed Welfare Games," Operations Research, INFORMS, vol. 61(1), pages 155-168, February.

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