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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- 喜多, 奈々緒
- 国立情報学研究所
書誌事項
- タイトル別名
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- Nonbipartite Dulmage-Mendelsohn Decomposition for Berge Duality (Foundations and Applications of Algorithms and Computation)
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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.
収録刊行物
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- 数理解析研究所講究録
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数理解析研究所講究録 2088 36-43, 2018-08
京都大学数理解析研究所
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詳細情報 詳細情報について
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- CRID
- 1050285299787405952
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- NII論文ID
- 120006861217
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- NII書誌ID
- AN00061013
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- ISSN
- 18802818
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- HANDLE
- 2433/251596
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- 本文言語コード
- en
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- 資料種別
- departmental bulletin paper
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- データソース種別
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- IRDB
- CiNii Articles