Modeling and Algorithms for Discrete Problems

2022 Fiscal Year Final Research Report

• Project/Area Number: 20K04978
• Research Category: Grant-in-Aid for Scientific Research (C)
• Allocation Type: Multi-year Fund
• Section: 一般
• Review Section: Basic Section 25010:Social systems engineering-related
• Research Institution: Kyoto University
• Principal Investigator: Haraguchi Kazuya 京都大学, 情報学研究科, 准教授 (80453356)
• Project Period (FY): 2020-04-01 – 2023-03-31
• Keywords: 列挙 / アルゴリズム理論 / 離散最適化

Outline of Final Research Achievements

It is the enumeration problem that we have made remarkable achievements. Suppose that a set system (i.e., a hypergraph) with an item set is implicitly given by means of an oracle that generates maximal solutions that are subsets of an input subset. We consider a problem that asks to enumerate all maximal solutions with respect to the common item set. We have developed polynomial-delay algorithms for a case when there is no assumption on the set system and a case when the set system is “confluent”. These results are so general that enabled us to find a way to new research problems that include implementation of algorithms that enumerate all maximal connected induced subgraphs with respect to the common itemset and enumeration of subgraphs that satisfy various connectivity conditions (e.g., 2-edge/vertex-connected induced subgraphs in undirected graphs and strongly-connected induced subgraphs in digraphs).

Free Research Field

数理工学

Academic Significance and Societal Importance of the Research Achievements

共通アイテム集合に関して極大解を列挙する問題を、従来まったく取り扱われてこなかった集合システム上に拡張し、多項式遅延列挙が可能であることを示した。この成果は、様々な連結性の条件について、共通アイテム集合に関して極大かつ当該連結条件を満たす誘導部分グラフを列挙することが、多項式遅延で可能なことを意味している。この問題は遺伝生物学において有意なタンパク質構造の発見や、DWAS分析などに応用を持ち、これら個別の問題を解決するための効率の良いアルゴリズムの存在が示唆されている。