ベルジュ双対のための非二部的Dulmage-Mendelsohn分解 (アルゴリズムと計算理論の基礎と応用)

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書誌事項

タイトル別名
  • Nonbipartite Dulmage-Mendelsohn Decomposition for Berge Duality (Foundations and Applications of Algorithms and Computation)

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抄録

The Dulmage-Mendelsohn decomposition is a classical canonical decomposition in matching theory applicable for bipartite graphs and is famous not only for its application in the field of matrix computation, but also for providing a prototypal structure in matroidal optimization theory. The Dulmage-Mendelsohn decomposition is stated and proved using the two color classes of a bipartite graph, and therefore generalizing this decomposition for nonbipartite graphs has been a difficult task. In our study, we obtain a new canonical decomposition that is a generalization of the Dulmage-Mendelsohn decomposition for arbitrary graphs using a recently introduced tool in matching theory, the basilica decomposition. Our result enables us to understand all known canonical decompositions in a unified way. Furthermore, we apply our result to derive a new theorem regarding barriers. The duality theorem for the maximum matching problem is the celebrated Berge formula, in which dual optimizers are known as barriers. Several results regarding maximal barriers have been derived by known canonical decompositions; however, no characterization has been known for general graphs. In our study, we provide a characterization of the family of maximal barriers in general graphs, in which the known results are developed and unified.

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詳細情報 詳細情報について

  • CRID
    1050285299787405952
  • NII論文ID
    120006861217
  • NII書誌ID
    AN00061013
  • ISSN
    18802818
  • HANDLE
    2433/251596
  • 本文言語コード
    en
  • 資料種別
    departmental bulletin paper
  • データソース種別
    • IRDB
    • CiNii Articles

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