Fixed width parameter algorithms for the graph isomorphism problem

• 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
• Project Status: Completed (Fiscal Year 2015)
• Budget Amount: ¥4,160,000 (Direct Cost: ¥3,200,000、Indirect Cost: ¥960,000); Fiscal Year 2015: ¥1,300,000 (Direct Cost: ¥1,000,000、Indirect Cost: ¥300,000); Fiscal Year 2014: ¥1,430,000 (Direct Cost: ¥1,100,000、Indirect Cost: ¥330,000); Fiscal Year 2013: ¥1,430,000 (Direct Cost: ¥1,100,000、Indirect Cost: ¥330,000)
• 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 / アルゴリズム理論 / 固定パラメータ容易性 / 木幅 / 木距離幅 / 禁止部分グラフ / 計算量二分法

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.

Research Products

• [Journal Article] A Polynomial-Time Approximation Scheme for the Geometric Unique Coverage Problem on Unit Squares (2016)
  • Author(s): Takehiro Ito, Shin-ichi Nakano, Yoshio Okamoto, Yota Otachi, Ryuhei Uehara, Takeaki Uno, Yushi Uno,
  • Journal Title: Computational Geometry: Theory and Applications Volume: 51 Pages: 25-39
  • DOI: 10.1016/j.comgeo.2015.10.004
  • NAID: 120005954496
  • Peer Reviewed
• [Journal Article] On the treewidth of toroidal grids (2016)
  • Author(s): Yoshio Okamoto, Masashi Kiyomi, and Yota Otachi
  • Journal Title: Discrete Applied Mathematics Volume: 198 Pages: 303-306
  • DOI: 10.1016/j.dam.2015.06.027
  • Peer Reviewed
• [Journal Article] Polynomial-time algorithms for Subgraph Isomorphism in small graph classes of perfect graphs (2016)
  • Author(s): Matsuo Konagaya, Yota Otachi, and Ryuhei Uehara
  • Journal Title: Discrete Applied Mathematics Volume: 199 Pages: 37-45
  • DOI: 10.1016/j.dam.2015.01.040
  • NAID: 120006380549
  • Peer Reviewed / Acknowledgement Compliant
• [Journal Article] Ferrers Dimension of Grid Intersection Graphs (2016)
  • Author(s): Steven Chaplick, Pavol Hell, Yota Otachi, Toshiki Saitoh, and Ryuhei Uehara
  • Journal Title: Discrete Applied Mathematics Volume: to appear Pages: 130-135
  • DOI: 10.1016/j.dam.2015.05.035
  • Peer Reviewed / Open Access / Int'l Joint Research
• [Journal Article] Extending partial representations of proper and unit interval graphs (2016)
  • Author(s): Pavel Klavik, Jan Kratochvil, Yota Otachi, Ignaz Rutter, Toshiki Saitoh, Maria Saumell, and Tomas Vyskocil
  • Journal Title: Algorithmica Volume: to appear Issue: 4 Pages: 1071-1104
  • DOI: 10.1007/s00453-016-0133-z
  • Peer Reviewed / Int'l Joint Research
• [Journal Article] Finding a chain graph in a bipartite permutation graph (2016)
  • Author(s): Masashi Kiyomi, Yota Otachi
  • Journal Title: Information Processing Letters Volume: 印刷中 Issue: 9 Pages: 569-573
  • DOI: 10.1016/j.ipl.2016.04.006
  • Peer Reviewed / Acknowledgement Compliant
• [Journal Article] Extending partial representations of subclasses of chordal graphs (2015)
  • Author(s): Pavel Klavik, Jan Kratochvil, Yota Otachi, and Toshiki Saitoh
  • Journal Title: Theoretical Computer Science Volume: 576 Pages: 85-101
  • DOI: 10.1016/j.tcs.2015.02.007
  • Peer Reviewed / Int'l Joint Research
• [Journal Article] Completely independent spanning trees in (partial) k-trees (2015)
  • Author(s): Masayoshi Matsushita, Yota Otachi, and Toru Araki
  • Journal Title: Discussiones Mathematicae Graph Theory Volume: 35 Issue: 3 Pages: 427-437
  • DOI: 10.7151/dmgt.1806
  • Peer Reviewed
• [Journal Article] Linear-Time Algorithm for Sliding Tokens on Trees (2015)
  • Author(s): Erik D Demaine, Martin L Demaine, Eli Fox-Epstein, Duc A Hoang, Takehiro Ito, Hirotaka Ono, Yota Otachi, Ryuhei Uehara, and Takeshi Yamada
  • Journal Title: Theoretical Computer Science Volume: 600 Pages: 132-142
  • DOI: 10.1016/j.tcs.2015.07.037
  • NAID: 120006355793
  • Peer Reviewed / Int'l Joint Research / Acknowledgement Compliant
• [Journal Article] Thin strip graphs (2015)
  • Author(s): T. Hayashi, A. Kawamura, Y. Otachi, H. Shinohara, and K. Yamazaki
  • Journal Title: Discrete Applied Mathematics, to appear Volume: - Pages: 203-210
  • DOI: 10.1016/j.dam.2015.01.018
  • Peer Reviewed / Open Access
• [Journal Article] Secure Sets and Defensive Alliances in Graphs: A Faster Algorithm and Improved Bounds (2015)
  • Author(s): Kazuyuki Amano, Kyaw May Oo, Yota Otachi, Ryuhei Uehara
  • Journal Title: IEICE Transactions on Information and Systems Volume: E98.D Issue: 3 Pages: 486-489
  • DOI: 10.1587/transinf.2014FCP0007
  • NAID: 130004841873
  • ISSN: 0916-8532, 1745-1361
  • Peer Reviewed / Acknowledgement Compliant
• [Journal Article] A 4.31-Approximation for the Geometric Unique Coverage Problem on Unit Disks (2014)
  • Author(s): Takehiro Ito, Shin-ichi Nakano, Yoshio Okamoto, Yota Otachi, Ryuhei Uehara, Takeaki Uno, Yushi Uno
  • Journal Title: Theoretical Computer Science Volume: 544 Pages: 14-31
  • DOI: 10.1016/j.tcs.2014.04.014
  • NAID: 120005893622
  • Peer Reviewed
• [Journal Article] Efficient algorithms for network localization using cores of underlying graphs (2014)
  • Author(s): Meng Li, Yota Otachi, Takeshi Tokuyama
  • Journal Title: Theoretical Computer Science Volume: 553 Pages: 18-26
  • DOI: 10.1016/j.tcs.2014.02.020
  • Peer Reviewed
• [Journal Article] Lower bounds for treewidth of product graphs (2014)
  • Author(s): Kyohei Kozawa, Yota Otachi, Koichi Yamazaki
  • Journal Title: Discrete Applied Mathematics Volume: 162 Pages: 251-258
  • DOI: 10.1016/j.dam.2013.08.005
  • Peer Reviewed
• [Journal Article] Approximating the path-distance-width for AT-free graphs and graphs in related classes (2013)
  • Author(s): Yota Otachi, Toshiki Saitoh, Katsuhisa Yamanaka, Shuji Kijima, Yoshio Okamoto, Hirotaka Ono, Yushi Uno, and Koichi Yamazaki
  • Journal Title: Discrete Applied Mathematics Volume: -- Pages: 69-77
  • DOI: 10.1016/j.dam.2012.11.015
  • Peer Reviewed
• [Journal Article] Base-object location problems for base-monotone regions (2013)
  • Author(s): J Chun, T. Horiyama, T. Ito, Natsuda Kaothanthong, H. Ono, Y. Otachi, T. Tokuyama, RUehara, and T. Uno
  • Journal Title: Theoretical Computer Science Volume: 555 Pages: 71-84
  • DOI: 10.1016/j.tcs.2013.11.030
  • Peer Reviewed / Open Access
• [Presentation] Sliding token on bipartite permutation graphs (2015)
  • Author(s): Eli Fox-Epstein, Duc A. Hoang, Yota Otachi, and Ryuhei Uehara
  • Organizer: 26th International Symposium on Algorithms and Computation (ISAAC 2015)
  • Place of Presentation: Nagoya Marriott Associa Hotel, Nagoya, Japan
  • Year and Date: 2015-12-09
  • Int'l Joint Research
• [Presentation] Swapping colored tokens on graphs (2015)
  • Author(s): Katsuhisa Yamanaka, Takashi Horiyama, David Kirkpatrick, Yota Otachi, Toshiki Saitoh, Ryuhei Uehara, and Yushi Uno
  • Organizer: 14th International Symposium on Algorithms and Data Structures (WADS 2015)
  • Place of Presentation: Victoria, BC, Canada
  • Year and Date: 2015-08-05
  • Int'l Joint Research
• [Presentation] Competitive diffusion on weighted graphs (2015)
  • Author(s): Takehiro Ito, Yota Otachi, Toshiki Saitoh, Hisayuki Satoh, Akira Suzuki, Kei Uchizawa, Ryuhei Uehara, Katsuhisa Yamanaka, and Xiao Zhou
  • Organizer: 14th International Symposium on Algorithms and Data Structures (WADS 2015)
  • Place of Presentation: Victoria, BC, Canada
  • Year and Date: 2015-08-05
  • Int'l Joint Research
• [Presentation] Induced minor free graphs: Isomorphism and clique-width (2015)
  • Author(s): Remy Belmonte, Yota Otachi, and Pascal Schweitzer
  • Organizer: 41st International Workshop on Graph-Theoretic Concepts in Computer Science (WG 2015)
  • Place of Presentation: Munich, Germany
  • Year and Date: 2015-07-17
  • Int'l Joint Research
• [Presentation] Reconfiguration of cliques in a graph (2015)
  • Author(s): Takehiro Ito, Hirotaka Ono, Yota Otachi
  • Organizer: 12th Annual Conference on Theory and Applications of Models of Computation (TAMC 2015)
  • Place of Presentation: Singapore
  • Year and Date: 2015-05-18
  • Int'l Joint Research
• [Presentation] Depth-first search using O(n) bits (2014)
  • Author(s): Tetsuo Asano, Taisuke Izumi, Masashi Kiyomi, Matsuo Konagaya, Hirotaka Ono, Yota Otachi, Pascal Schweitzer, Jun Tarui, and Ryuhei Uehara
  • Organizer: 25th International Symposium on Algorithms and Computation (ISAAC 2014)
  • Place of Presentation: Jeonju, Korea
  • Year and Date: 2014-12-15 – 2014-12-17
• [Presentation] Polynomial-time algorithm for sliding tokens on trees (2014)
  • Author(s): Erik D. Demaine, Martin L. Demaine, Eli Fox-Epstein, Duc A. Hoang, Takehiro Ito, Hirotaka Ono, Yota Otachi, Ryuhei Uehara, and Takeshi Yamada
  • Organizer: 25th International Symposium on Algorithms and Computation (ISAAC 2014)
  • Place of Presentation: Jeonju, Korea
  • Year and Date: 2014-12-15 – 2014-12-17
• [Presentation] Extending partial representations of proper and unit interval graphs (2014)
  • Author(s): Pavel Klavik, Jan Kratochvil, Yota Otachi, Ignaz Rutter, Toshiki Saitoh, Maria Saumell, and Tomas Vyskocil
  • Organizer: 14th Scandinavian Symposium and Workshops on Algorithm Theory (SWAT 2014)
  • Place of Presentation: Copenhagen, Denmark
  • Year and Date: 2014-07-02 – 2014-07-04
• [Presentation] Reduction techniques for graph isomorphism in the context of width parameters (2014)
  • Author(s): Yota Otachi and Pascal Schweitzer
  • Organizer: 14th Scandinavian Symposium and Workshops on Algorithm Theory (SWAT 2014)
  • Place of Presentation: Copenhagen, Denmark
  • Year and Date: 2014-07-02 – 2014-07-04
• [Presentation] Polynomial-time algorithms for subgraph isomorphism in small graph classes of perfect graphs (2014)
  • Author(s): Matsuo Konagaya, Yota Otachi, and Ryuhei Uehara
  • Organizer: 11th Annual Conference on Theory and Applications of Models of Computation (TAMC 2014)
  • Place of Presentation: Chennai, India
  • Year and Date: 2014-04-11 – 2014-04-13
• [Presentation] Intersection dimension of bipartite graphs (2014)
  • Author(s): Steven Chaplick, Pavol Hell, Yota Otachi, Toshiki Saitoh, and Ryuhei Uehara
  • Organizer: 11th Annual Conference on Theory and Applications of Models of Computation (TAMC 2014)
  • Place of Presentation: Chennai, India
  • Year and Date: 2014-04-11 – 2014-04-13
• [Presentation] Isomorphism on subgraph-closed graph classes: a complexity dichotomy and intermediate graph classes (2013)
  • Author(s): Yota Otachi and Pascal Schweitzer
  • Organizer: 24th International Symposium on Algorithms and Computation (ISAAC 2013)
  • Place of Presentation: Hong Kong, China
• [Presentation] Bounded representations of interval and proper interval graphs (2013)
  • Author(s): Martin Balko, Pavel Klavik, and Yota Otachi
  • Organizer: 24th International Symposium on Algorithms and Computation (ISAAC 2013)
  • Place of Presentation: Hong Kong, China
• [Presentation] On low congestion spanning trees (2013)
  • Author(s): Yota Otachi
  • Organizer: 8th Japanese-Hungarian Symposium on Discrete Mathematics and Its Applications
  • Place of Presentation: Veszprem, Hungary
  • Invited