論文

査読有り
2019年

A tractable class of binary VCSPs via M-convex intersection

ACM Transactions on Algorithms
  • Hiroshi Hirai
  • ,
  • Yuni Iwamasa
  • ,
  • Kazuo Murota
  • ,
  • Stanislav Živný

15
3
開始ページ
44:1
終了ページ
44:41
記述言語
掲載種別
研究論文(学術雑誌)
DOI
10.1145/3329862
出版者・発行元
Association for Computing Machinery (ACM)

A binary VCSP is a general framework for the minimization problem of a function represented as the sum of unary and binary cost functions. An important line of VCSP research is to investigate what functions can be solved in polynomial time. Cooper and Živný classified the tractability of binary VCSP instances according to the concept of “triangle,” and showed that the only interesting tractable case is the one induced by the joint winner property (JWP). Recently, Iwamasa, Murota, and Živný made a link between VCSP and discrete convex analysis, showing that a function satisfying the JWP can be transformed into a function represented as the sum of two quadratic M-convex functions, which can be minimized in polynomial time via an M-convex intersection algorithm if the value oracle of each M-convex function is given.

In this article, we give an algorithmic answer to a natural question: What binary finite-valued CSP instances can be represented as the sum of two quadratic M-convex functions and can be solved in polynomial time via an M-convex intersection algorithm? We solve this problem by devising a polynomial-time algorithm for obtaining a concrete form of the representation in the representable case. Our result presents a larger tractable class of binary finite-valued CSPs, which properly contains the JWP class.

リンク情報
DOI
https://doi.org/10.1145/3329862
URL
https://dl.acm.org/doi/pdf/10.1145/3329862
ID情報
  • DOI : 10.1145/3329862
  • ISSN : 1549-6325
  • eISSN : 1549-6333

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