Fixed width parameter algorithms for the graph isomorphism problem

2015 Fiscal Year Final Research Report

• Project/Area Number: 25730003
• Research Category: Grant-in-Aid for Young Scientists (B)
• Allocation Type: Multi-year Fund
• Research Field: Theory of informatics
• Research Institution: Japan Advanced Institute of Science and Technology
• Principal Investigator: Otachi Yota 北陸先端科学技術大学院大学, 情報科学研究科, 助教 (80610196)
• Project Period (FY): 2013-04-01 – 2016-03-31
• Keywords: グラフアルゴリズム / グラフ同型性判定問題 / グラフ幅パラメータ

Outline of Final Research Achievements

We showed that the graph isomorphism problem is fixed-parameter tractable when parameterized by root-connected tree distance width. To show the result, we modified the classic Weisfeiler-Lehman algorithm so that it works not only for all vertex subsets of size k but also for restricted family of vertex subsets of size k. Furthermore, the modified algorithm runs in FPT time with the parameter k. Then we showed that we can apply the algorithm to the graph isomorphism problem parmeterized by several graph width parameters including root-connected tree distance width.
We also studied the graph isomorphism problem for graph classes forbidding a single graph as an induced minor. We showed a complexity dichotomy with respect to the forbidden induced minor.

Free Research Field

グラフアルゴリズム