On the approximability of the maximum feasible subsystem problem with 0/1-coefficients

Khaled Elbassioni, Rajiv Raman, Saurabh Ray, René Sitters

    Research output: Chapter in Book/Report/Conference proceedingConference contribution

    Abstract

    Given a system of constraints ℓi ≤ ai T x ≤ ui, where ai ∈ {0,1}n, and ℓi, ui ∈ ℝ+, for i = 1, . . . , m, we consider the problem MRFS of finding the largest subsystem for which there exists a feasible solution x ≥ 0. We present approximation algorithms and inapproximability results for this problem, and study some important special cases. Our main contributions are : 1. In the general case, where ai ∈ {0, 1}n, a sharp separation in the approximability between the case when L = max{ℓ1, . . . , ℓm} is bounded above by a polynomial in n and m, and the case when it is not. 2. In the case where A is an interval matrix, a sharp separation in approximability between the case where we allow a violation of the upper bounds by at most a (1 + ∈) factor, for any fixed ∈ > 0 and the case where no violations are allowed. Along the way, we prove that the induced matching problem on bipartite graphs is inapproximable beyond a factor of Ω(n1/3-∈), for any ∈ > 0 unless NP=ZPP. Finally, we also show applications of MRFS to some recently studied pricing problems.

    Original languageEnglish (US)
    Title of host publicationProceedings of the 20th Annual ACM-SIAM Symposium on Discrete Algorithms
    Pages1210-1219
    Number of pages10
    StatePublished - Sep 21 2009
    Event20th Annual ACM-SIAM Symposium on Discrete Algorithms - New York, NY, United States
    Duration: Jan 4 2009Jan 6 2009

    Other

    Other20th Annual ACM-SIAM Symposium on Discrete Algorithms
    CountryUnited States
    CityNew York, NY
    Period1/4/091/6/09

    Fingerprint

    Approximability
    Inapproximability
    Subsystem
    Approximation algorithms
    Coefficient
    Induced Matching
    Interval Matrix
    Polynomials
    Matching Problem
    Bipartite Graph
    Pricing
    Approximation Algorithms
    Upper bound
    Costs
    Polynomial

    ASJC Scopus subject areas

    • Software
    • Mathematics(all)

    Cite this

    Elbassioni, K., Raman, R., Ray, S., & Sitters, R. (2009). On the approximability of the maximum feasible subsystem problem with 0/1-coefficients. In Proceedings of the 20th Annual ACM-SIAM Symposium on Discrete Algorithms (pp. 1210-1219)

    On the approximability of the maximum feasible subsystem problem with 0/1-coefficients. / Elbassioni, Khaled; Raman, Rajiv; Ray, Saurabh; Sitters, René.

    Proceedings of the 20th Annual ACM-SIAM Symposium on Discrete Algorithms. 2009. p. 1210-1219.

    Research output: Chapter in Book/Report/Conference proceedingConference contribution

    Elbassioni, K, Raman, R, Ray, S & Sitters, R 2009, On the approximability of the maximum feasible subsystem problem with 0/1-coefficients. in Proceedings of the 20th Annual ACM-SIAM Symposium on Discrete Algorithms. pp. 1210-1219, 20th Annual ACM-SIAM Symposium on Discrete Algorithms, New York, NY, United States, 1/4/09.
    Elbassioni K, Raman R, Ray S, Sitters R. On the approximability of the maximum feasible subsystem problem with 0/1-coefficients. In Proceedings of the 20th Annual ACM-SIAM Symposium on Discrete Algorithms. 2009. p. 1210-1219
    Elbassioni, Khaled ; Raman, Rajiv ; Ray, Saurabh ; Sitters, René. / On the approximability of the maximum feasible subsystem problem with 0/1-coefficients. Proceedings of the 20th Annual ACM-SIAM Symposium on Discrete Algorithms. 2009. pp. 1210-1219
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