### Abstract

Given a system of constraints ℓ_{i} ≤ a_{i} ^{T} x ≤ u_{i}, where a_{i} ∈ {0,1}^{n}, and ℓ_{i}, u_{i} ∈ 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 a_{i} ∈ {0, 1}^{n}, a sharp separation in the approximability between the case when L = max{ℓ_{1}, . . . , ℓ_{m}} 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(n^{1/3-∈}), for any ∈ > 0 unless NP=ZPP. Finally, we also show applications of MRFS to some recently studied pricing problems.

Original language | English (US) |
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Title of host publication | Proceedings of the 20th Annual ACM-SIAM Symposium on Discrete Algorithms |

Pages | 1210-1219 |

Number of pages | 10 |

State | Published - Sep 21 2009 |

Event | 20th Annual ACM-SIAM Symposium on Discrete Algorithms - New York, NY, United States Duration: Jan 4 2009 → Jan 6 2009 |

### Other

Other | 20th Annual ACM-SIAM Symposium on Discrete Algorithms |
---|---|

Country | United States |

City | New York, NY |

Period | 1/4/09 → 1/6/09 |

### Fingerprint

### ASJC Scopus subject areas

- Software
- Mathematics(all)

### Cite this

*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.

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution

*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.

}

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 - 2009/9/21

Y1 - 2009/9/21

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.

UR - http://www.scopus.com/inward/record.url?scp=70349129490&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=70349129490&partnerID=8YFLogxK

M3 - Conference contribution

SN - 9780898716801

SP - 1210

EP - 1219

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

ER -