A primal-simplex based Tardos’ algorithm

In the mid-eighties Tardos proposed a strongly polynomial algorithm for solving linear programming problems for which the size of the coefficient matrix is polynomially bounded in the dimension of the input. Combining Orlin’s primal-based modification and Mizuno’s use of the simplex method, we intro...

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Bibliographic Details
Published in:Operations research letters Vol. 43; no. 6; pp. 625 - 628
Main Authors: Mizuno, Shinji, Sukegawa, Noriyoshi, Deza, Antoine
Format: Journal Article
Language:English
Published: Elsevier B.V 01.11.2015
Elsevier
Subjects:
Combinatorics
Computational Geometry
Computer Science
Discrete Mathematics
Mathematics
Optimization and Control
Simplex method
Strongly polynomial algorithm
Tardos’ algorithm
Total unimodularity
Strongly polynomial algorithm
Total unimodularity
Tardos’ algorithm
Simplex method
ISSN:0167-6377, 1872-7468
Online Access:Get full text
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Summary:In the mid-eighties Tardos proposed a strongly polynomial algorithm for solving linear programming problems for which the size of the coefficient matrix is polynomially bounded in the dimension of the input. Combining Orlin’s primal-based modification and Mizuno’s use of the simplex method, we introduce a modification of Tardos’ algorithm considering only the primal problem and using the simplex method to solve the auxiliary problems. The proposed algorithm is strongly polynomial if the coefficient matrix is totally unimodular and the auxiliary problems are non-degenerate.
ISSN:0167-6377
1872-7468
DOI:10.1016/j.orl.2015.10.002