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Main Title: Proximity bounds for random integer programs
Author(s): Celaya, Marcel
Henk, Martin
Type: Research Paper
Abstract: We study proximity bounds within a natural model of random integer programs of the type max cx : Ax = b, X œ Z >= 0, where A œ Z^mXn of rank m, b œ Z^m and c œ Z^n. We prove that (up to a constant depending on the dimension n) the proximity is generally bounded by ∆m(A)^1/(n-m), where ∆m(A) is the maximal absolute value of an m x m subdeterminant of A. This is significantly better than the best deterministic bounds which are linear in ∆m(A).
Subject(s): Integer programming
lattices in n dimensions
convex bodies in n dimensions
Issue Date: 11-Dec-2020
Date Available: 17-Dec-2021
Language Code: en
DDC Class: 510 Mathematik
MSC 2000: integer programming
lattices in n dimensions
convex bodies in n dimensions
Series: Preprint-Reihe des Instituts für Mathematik, Technische Universität Berlin
Series Number: 2020, 05
ISSN: 2197-8085
TU Affiliation(s): Fak. 2 Mathematik und Naturwissenschaften » Inst. Mathematik
Appears in Collections:Technische Universität Berlin » Publications

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