Research on Design Method of Graph Algorithm based on Tree Structure

2018 Fiscal Year Final Research Report

• Project/Area Number: 16K00003
• Research Category: Grant-in-Aid for Scientific Research (C)
• Allocation Type: Multi-year Fund
• Section: 一般
• Research Field: Theory of informatics
• Research Institution: Tohoku University
• Principal Investigator: Zhou Xiao 東北大学, 情報科学研究科, 教授 (10272022)
• Project Period (FY): 2016-04-01 – 2019-03-31
• Keywords: グラフ / 木 / 木幅 / アルゴリズム / 木分解 / 組合せ問題

Outline of Final Research Achievements

The results obtained in this research are theoretical development of efficient algorithms for graphs with small tree-widths. The tree-width of a graph is the maximum value obtained by subtracting 1 from the number of vertices in nodes of its tree-decomposition. The graph of tree-width 1 is a forest, and the graph of tree-width 2 is series-parallel. In this research, in particular, we succeeded in researching and developing efficient algorithms for solving many combinatoric optimal problems by introducing graph division and clever dynamic programming to a graph having a tree structure. In particular, the algorithms developed in this research are applicable to many combinatoric problems, and we have published 12 academic papers summarizing the results obtained in this research, which can be highly appreciated.

Free Research Field

理論計算機科学

Academic Significance and Societal Importance of the Research Achievements

学術的貢献として，グラフ特に木や直並列グラフや木幅が小さいグラフに関する理論的な展開とアルゴリズムの効率化があげられる．グラフアルゴリズムに関する成果はこの3年間に12編の論文として一流国際学術誌や国際会議で発表されている．これらのアルゴリズムの開発で導入された手法は多くの組合せ問題に応用可能であり，理論計算機科学分野の重要な成果である．