A polynomial oracle-time algorithm for convex integer minimization

In this paper we consider the solution of certain convex integer minimization problems via greedy augmentation procedures. We show that a greedy augmentation procedure that employs only directions from certain Graver bases needs only polynomially many augmentation steps to solve the given problem. W...

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Bibliographic Details
Published in:	Mathematical programming Vol. 126; no. 1; pp. 97 - 117
Main Authors:	Hemmecke, Raymond, Onn, Shmuel, Weismantel, Robert
Format:	Journal Article
Language:	English
Published:	Berlin/Heidelberg Springer-Verlag 01.01.2011 Springer Springer Nature B.V
Subjects:	Algorithmics. Computability. Computer arithmetics Algorithms Applied sciences Augmentation Calculus of Variations and Optimal Control; Optimization Circuits Combinatorics Computer science; control theory; systems Convex analysis Convex and discrete geometry Exact sciences and technology Full Length Paper Geometry Information retrieval. Graph Integer programming Integers Mathematical analysis Mathematical and Computational Physics Mathematical Methods in Physics Mathematical programming Mathematics Mathematics and Statistics Mathematics of Computing Minimization Multivariate analysis Numerical Analysis Optimization Polynomials Probability and statistics Sciences and techniques of general use Statistics Stochasticity Studies Theorems Theoretical Theoretical computing 68R 68U 52B 68W 52C 90B 62H 90C 68Q Polytope Statistical analysis Probabilistic approach Minimization Multivariate analysis Convex programming Polynomial time Integer programming Discrete geometry Oracle
ISSN:	0025-5610, 1436-4646
Online Access:	Get full text
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