TY - GEN

T1 - On the approximability of the maximum feasible subsystem problem with 0/1-coefficients

AU - Elbassioni, Khaled

AU - Raman, Rajiv

AU - Ray, Saurabh

AU - Sitters, René

PY - 2009

Y1 - 2009

N2 - 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.

AB - 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.

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U2 - 10.1137/1.9781611973068.131

DO - 10.1137/1.9781611973068.131

M3 - Conference contribution

AN - SCOPUS:70349129490

SN - 9780898716801

T3 - Proceedings of the Annual ACM-SIAM Symposium on Discrete Algorithms

SP - 1210

EP - 1219

BT - Proceedings of the 20th Annual ACM-SIAM Symposium on Discrete Algorithms

PB - Association for Computing Machinery (ACM)

T2 - 20th Annual ACM-SIAM Symposium on Discrete Algorithms

Y2 - 4 January 2009 through 6 January 2009

ER -