Trichotomy for the reconfiguration problem of integer linear systems

Kei Kimura, Akira Suzuki

研究成果: Chapter in Book/Report/Conference proceedingConference contribution

1 被引用数 (Scopus)

抄録

In this paper, we consider the reconfiguration problem of integer linear systems. In this problem, we are given an integer linear system I and two feasible solutions s and t of I, and then asked to transform s to t by changing a value of only one variable at a time, while maintaining a feasible solution of I throughout. Z(I) for I is the complexity index introduced by Kimura and Makino (Discrete Applied Mathematics 200:67–78, 2016), which is defined by the sign pattern of the input matrix. We analyze the complexity of the reconfiguration problem of integer linear systems based on the complexity index Z(I) of given I. We show that the problem is (i) solvable in constant time if Z(I) is less than one, (ii) weakly coNP-complete and pseudo-polynomially solvable if Z(I) is exactly one, and (iii) PSPACE-complete if Z(I) is greater than one. Since the complexity indices of Horn and two-variable-par-inequality integer linear systems are at most one, our results imply that the reconfiguration of these systems are in coNP and pseudo-polynomially solvable. Moreover, this is the first result that reveals coNP-completeness for a reconfiguration problem, to the best of our knowledge.

本文言語英語
ホスト出版物のタイトルWALCOM
ホスト出版物のサブタイトルAlgorithms and Computation - 14th International Conference, WALCOM 2020, Proceedings
編集者M. Sohel Rahman, Kunihiko Sadakane, Wing-Kin Sung
出版社Springer
ページ336-341
ページ数6
ISBN(印刷版)9783030398804
DOI
出版ステータス出版済み - 2020
外部発表はい
イベント14th International Conference and Workshops on Algorithms and Computation, WALCOM 2020 - Singapore, シンガポール
継続期間: 3 31 20204 2 2020

出版物シリーズ

名前Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
12049 LNCS
ISSN(印刷版)0302-9743
ISSN(電子版)1611-3349

会議

会議14th International Conference and Workshops on Algorithms and Computation, WALCOM 2020
国/地域シンガポール
CitySingapore
Period3/31/204/2/20

All Science Journal Classification (ASJC) codes

  • 理論的コンピュータサイエンス
  • コンピュータ サイエンス(全般)

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