Combinatorial Relaxation Algorithm for the Entire Sequence of the Maximum Degree of Minors

This paper presents an efficient “combinatorial relaxation” algorithm for computing the entire sequence of the maximum degree of minors in rational function matrices, whereas the previous algorithms find them separately for a specified order k . The efficiency of the algorithm is based on the discre...

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Published in:	Algorithmica Vol. 77; no. 3; pp. 815 - 835
Main Author:	Sato, Shun
Format:	Journal Article
Language:	English
Published:	New York Springer US 01.03.2017 Springer Nature B.V
Subjects:	Algorithm Analysis and Problem Complexity Algorithms Combinatorial analysis Computer Science Computer Systems Organization and Communication Networks Concavity Data Structures and Information Theory Mathematics of Computing Rational functions Theory of Computation Degree of minor Valuated bimatroid 90C27 Combinatorial relaxation Discrete concavity
ISSN:	0178-4617, 1432-0541
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Abstract	This paper presents an efficient “combinatorial relaxation” algorithm for computing the entire sequence of the maximum degree of minors in rational function matrices, whereas the previous algorithms find them separately for a specified order k . The efficiency of the algorithm is based on the discrete concavity related to valuated bimatroids.
AbstractList	This paper presents an efficient “combinatorial relaxation” algorithm for computing the entire sequence of the maximum degree of minors in rational function matrices, whereas the previous algorithms find them separately for a specified order k . The efficiency of the algorithm is based on the discrete concavity related to valuated bimatroids. This paper presents an efficient “combinatorial relaxation” algorithm for computing the entire sequence of the maximum degree of minors in rational function matrices, whereas the previous algorithms find them separately for a specified order k. The efficiency of the algorithm is based on the discrete concavity related to valuated bimatroids.
Author	Sato, Shun
Author_xml	– sequence: 1 givenname: Shun surname: Sato fullname: Sato, Shun email: shun_sato@mist.i.u-tokyo.ac.jp organization: Department of Mathematical Informatics, Graduate School of Information Science and Technology, University of Tokyo
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SubjectTerms	Algorithm Analysis and Problem Complexity Algorithms Combinatorial analysis Computer Science Computer Systems Organization and Communication Networks Concavity Data Structures and Information Theory Mathematics of Computing Rational functions Theory of Computation
Title	Combinatorial Relaxation Algorithm for the Entire Sequence of the Maximum Degree of Minors
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