Advances in Theory and Design Principles of Counting AlgorithmsBased on Polyhedral Combinatorics

2011 Fiscal Year Final Research Report

• Project/Area Number: 21700009
• Research Category: Grant-in-Aid for Young Scientists (B)
• Allocation Type: Single-year Grants
• Research Field: Fundamental theory of informatics
• Research Institution: The University of Electro-Communications (2011); Japan Advanced Institute of Science and Technology (2010); Tokyo Institute of Technology (2009)
• Principal Investigator: OKAMOTO Yoshio 電気通信大学, 大学院・情報理工学研究科, 准教授 (00402660)
• Project Period (FY): 2009 – 2011
• Keywords: アルゴリズム / 離散数学 / 凸多面体 / グラフ / 離散幾何

Research Abstract

Results on counting problems for graphs, counting problems for discrete and computational geometry, and their applications to optimization problems were obtained. For example, the computational complexity of counting the dominating sets in a graph was investigated from the perspective of graph classes, and a polynomial-time algorithm to find a global optimal solution to the distance function maximization was developed by efficiently enumerating all local optimal solutions. These results were presented in refereed international journals and refereed international conferences.

Research Products

• [Journal Article] On bipartite powers of bigraphs (2012)
  • Author(s): Yoshio Okamoto, Yota Otachi, and Ryuhei Uehara
  • Journal Title: Discrete Mathematics & Theoretical Computer Science Volume: 14(2) Pages: 11-20
  • URL: http://www.dmtcs.org/dmtcs-ojs/index.php/dmtcs/article/view/2132
  • Peer Reviewed
• [Journal Article] Reverse preferential spread in complex networks (2012)
  • Author(s): Hiroshi Toyoizumi, Seiichi Tani, Naoto Miyoshi, and Yoshio Okamoto
  • Journal Title: Physical Review E Volume: 86 Pages: 021103
  • URL: http://dx.doi.org/10.1103/PhysRevE.86.021103
  • Peer Reviewed
• [Journal Article] Minimum and maximum against k lies (2012)
  • Author(s): Michael Hoffmann, Jiri Matousek, Yoshio Okamoto, and Philipp Zumstein
  • Journal Title: Chicago Journal of Theoretical Computer Science 2012 Volume: Article 2 Pages: 1-10
  • URL: http://dx.doi.org/10.4086/cjtcs.2012.002
  • Peer Reviewed
• [Journal Article] Vertex angle and crossing angle resolution of leveled tree drawings (2012)
  • Author(s): Walter Didimo, Michael Kaufmann, Giuseppe Liotta, Yoshio Okamoto, and Andreas Spillner
  • Journal Title: Information Processing Letters Volume: 112 Pages: 630-635
  • URL: http://dx.doi.org/10.1016/j.ipl.2012.05.006
  • Peer Reviewed
• [Journal Article] Querying two boundary points for shortest paths in a polygonal domain (2012)
  • Author(s): Sang Won Bae and Yoshio Okamoto
  • Journal Title: Computational Geometry: Theory and Applications Volume: 45 Pages: 284-293
  • URL: http://dx.doi.org/10.1016/j.comgeo.2012.01.012
  • Peer Reviewed
• [Journal Article] Drawing (complete) binary tanglegrams: Hardness, approximation (2012)
  • Author(s): Kevin Buchin, Maike Buchin, Jaroslaw Byrka, Martin Nollenburg, Yoshio Okamoto, Rodrigo I. Silveira, and Alexander Wolff
  • Journal Title: fixed-parameter tractability. Algorithmica Volume: 62 Pages: 309-332
  • URL: http://dx.doi.org/10.1007/s00453-010-9456-3
  • Peer Reviewed
• [Journal Article] Area bounds of rectilinear polygons realized by angle sequences. (2012)
  • Author(s): Sang Won Bae, Yoshio Okamoto, and Chan-Su Shin
  • Journal Title: Lecture Notes in Computer Science Volume: 7676 Pages: 629-638
  • URL: http://dx.doi.org/10.1007/978-3-642-35261-4_65
  • Peer Reviewed
• [Journal Article] Giuseppe Liotta Tamara Mchedlidze, Henk Meijer, and Yoshio Okamoto (2012)
  • Author(s): Patrizio Angelini, Carla Binucci, William Evans, Ferran Hurtado
  • Journal Title: Universal point subsets for planar graphs. Lecture Notes in Computer Science Volume: 7676 Pages: 423-432
  • URL: http://dx.doi.org/10.1007/978-3-642-35261-4_45
  • Peer Reviewed
• [Journal Article] A4.31-approximation for the geometric unique coverage problem on unit disks (2012)
  • Author(s): Takehiro Ito, Shin-Ichi Nakano, Yoshio Okamoto, Yota Otachi, Ryuhei Uehara, Takeaki Uno, and Yushi Uno
  • Journal Title: Lecture Notes in Computer Science Volume: 7676 Pages: 372-381
  • URL: http://dx.doi.org/10.1007/978-3-642-35261-4_40
  • Peer Reviewed
• [Journal Article] On problems as hard as CNF-SAT (2012)
  • Author(s): Marek Cygan, Holger Dell, Daniel Lokshtanov, Daniel Marx, Jesper Nederlof, Yoshio Okamoto, Ramamohan Paturi, Saket Saurabh, and Magnus Wahlstrom
  • Journal Title: Proceedings of27th IEEE Conference onComputational Complexity (CCC 2012) Pages: 74-84
  • URL: http://dx.doi.org/10.1109/CCC.2012.36
  • Peer Reviewed
• [Journal Article] A polynomial-time approximation scheme for the geometric unique coverage problem on unit squares. (2012)
  • Author(s): Takehiro Ito, Shin-Ichi Nakano, Yoshio Okamoto, Yota Otachi, Ryuhei Uehara, Takeaki Uno, and Yushi Uno
  • Journal Title: Lecture Notes in Computer Science Volume: 7357 Pages: 24-35
  • URL: http://dx.doi.org/10.1007/978-3-642-31155-0_3
  • Peer Reviewed
• [Journal Article] Efficient enumeration of the directed binary perfect phylogenies from incomplete data. (2012)
  • Author(s): Masashi Kiyomi, Yoshio Okamoto, and Toshiki Saitoh
  • Journal Title: Lecture Notes in Computer Science Volume: 7276 Pages: 248-259
  • URL: http://dx.doi.org/10.1007/978-3-642-30850-5_22
  • Peer Reviewed
• [Journal Article] Hardness results and an exact exponential algorithm for the spanning tree congestion problem (2011)
  • Author(s): Yoshio Okamoto, Yota Otachi, Ryuhei Uehara, and Takeaki Uno
  • Journal Title: Journal of Graph Algorithms and Applications Volume: 15 Pages: 727-751
  • URL: http://jgaa.info/accepted/2011/OkamotoOtachiUeharaUno
  • Peer Reviewed
• [Journal Article] The t-pebbling number is eventually linear in t (2011)
  • Author(s): Michael Hoffmann, Jiri Matousek, Yoshio Okamoto, and Philipp Zumstein
  • Journal Title: The Electronic Journal of Comb Volume: 18(1) Pages: 153
  • URL: http://www.combinatorics.org/Volume_18/Abstracts/v18i1p153.html
  • Peer Reviewed
• [Journal Article] Adaptive algorithms for planar convex hull problems (2011)
  • Author(s): Hee-Kap Ahn and Yoshio Okamoto
  • Journal Title: IEICE Transactions on Information and Systems Volume: E94-D Pages: 182-189
  • URL: http://dx.doi.org/10.1587/transinf.E94.D.182
  • Peer Reviewed
• [Journal Article] Apolynomial-time-delaypolynomial-space algorithm for enumeration problems in multi-criteria optimization. (2011)
  • Author(s): Yoshio Okamoto and Takeaki Uno
  • Journal Title: European Journal of Operational Research Volume: 210 Pages: 48-56
  • URL: http://dx.doi.org/10.1016/j.ejor.2010.10.008
  • Peer Reviewed
• [Journal Article] Submodular fractional programming for balanced clustering (2011)
  • Author(s): Yoshinobu Kawahara, Kiyohito Nagano, and Yoshio Okamoto
  • Journal Title: Pattern Recognition Letters Volume: 32 Pages: 235-243
  • URL: http://dx.doi.org/10.1016/j.patrec.2010.08.008
  • Peer Reviewed
• [Journal Article] Approximability of the path-distance-width for AT-free graphs (2011)
  • Author(s): Yota Otachi, Toshiki Saitoh, Katsuhisa Yamanaka, Shuji Kijima, Yoshio Okamoto, Hirotaka Ono, Yushi Uno, and Koichi Yamazaki
  • Journal Title: Lecture Notes in Computer Science Volume: 6986 Pages: 271-282
  • URL: http://dx.doi.org/10.1007/978-3-642-25870-1_25
  • Peer Reviewed
• [Journal Article] Dominating set counting in graph classes (2011)
  • Author(s): Shuji Kijima, Yoshio Okamoto, and Takeaki Uno
  • Journal Title: Lecture Notes in Computer Science Volume: 6842 Pages: 13-24
  • URL: http://dx.doi.org/10.1007/978-3-642-22685-4_2
  • Peer Reviewed
• [Journal Article] Hardness results and an exact exponential algorithm for the spanning tree congestion problem (2011)
  • Author(s): Yoshio Okamoto, Yota Otachi, Ryuhei Uehara, and Takeaki Uno
  • Journal Title: Lecture Notes in Computer Science Volume: 6648 Pages: 452-462
  • URL: http://dx.doi.org/10.1007/978-3-642-20877-5_44
  • Peer Reviewed
• [Journal Article] A tight lower bound for convexly independent subsets of the Minkowski sums of planar point sets (2010)
  • Author(s): Ondrej Bilka, Kevin Buchin, Radoslav Fulek, Masashi Kiyomi, Yoshio Okamoto, Shin-ichi Tanigawa, and Csaba D. Toth
  • Journal Title: The Electronic Journal of Combinatorics Volume: 17 Pages: N35
  • URL: http://www.combinatorics.org/Volume_17/Abstracts/v17i1n35.html
  • Peer Reviewed
• [Journal Article] On listing, sampling, and counting the chordal graphs with edge constraints. (2010)
  • Author(s): Shuji Kijima, Masashi Kiyomi, Yoshio Okamoto, and Takeaki Uno
  • Journal Title: Theoretical Computer Science Volume: 411 Pages: 2591-2601
  • URL: http://dx.doi.org/10.1016/j.tcs.2010.03.024
  • Peer Reviewed
• [Journal Article] Improved bounds for wireless localization (2010)
  • Author(s): Tobias Christ, Michael Hoffmann, Yoshio Okamoto, and Takeaki Uno
  • Journal Title: Algorithmica Volume: 57 Pages: 499-516
  • URL: http://dx.doi.org/10.1007/s00453-009-9287-2
  • Peer Reviewed
• [Journal Article] The geodesic diameter of polygonal domains (2010)
  • Author(s): Sang Won Bae, Matias Korman, and Yoshio Okamoto
  • Journal Title: Lecture Notes in Computer Science Volume: 6346 Pages: 500-511
  • URL: http://dx.doi.org/10.1007/978-3-642-15775-2_43
  • Peer Reviewed
• [Journal Article] Adaptive algorithms for planar convex hull problems (2010)
  • Author(s): Hee-Kap Ahn and Yoshio Okamoto
  • Journal Title: Lecture Notes in Computer Science Volume: 6213 Pages: 316-326
  • URL: http://dx.doi.org/10.1007/978-3-642-14553-7_30
  • Peer Reviewed
• [Journal Article] Minimum and maximum against k lies (2010)
  • Author(s): Michael Hoffmann, Jiri Matousek, Yoshio Okamoto, and Philipp Zumstein
  • Journal Title: Lecture Notes in Computer Science Volume: 6139 Pages: 139-149
  • URL: http://dx.doi.org/10.1007/978-3-642-13731-0_14
  • Peer Reviewed
• [Journal Article] Counting the number of matchings in chordal and chordal bipartite graph classes (2010)
  • Author(s): Yoshio Okamoto, Ryuhei Uehara, and Takeaki Uno
  • Journal Title: Lecture Notes in Computer Science Volume: 5911 Pages: 296-307
  • URL: http://dx.doi.org/10.1007/978-3-642-11409-0_26
  • Peer Reviewed
• [Journal Article] Untangling a planar graph (2009)
  • Author(s): Xavier Goaoc, Jan Kratochvil, Yoshio Okamoto, Chan-Su Shin, Andreas Spillner, andAlexander Wolff.
  • Journal Title: Discrete& Computational Geometry Volume: 42 Pages: 542-569
  • URL: http://dx.doi.org/10.1007/s00454-008-9130-6
  • Peer Reviewed
• [Journal Article] The Holt-Klee condition for oriented matroids (2009)
  • Author(s): Komei Fukuda, Sonoko Moriyama, and Yoshio Okamoto
  • Journal Title: European Journal of Combinatorics Volume: 30 Pages: 1854-1867
  • URL: http://dx.doi.org/10.1016/j.ejc.2008.12.012
  • Peer Reviewed
• [Journal Article] Querying two boundary points for shortest paths in a polygonal domain (2009)
  • Author(s): Sang Won Bae and Yoshio Okamoto
  • Journal Title: Lecture Notes in Computer Science Volume: 5878 Pages: 1054-1063
  • URL: http://dx.doi.org/10.1007/978-3-642-10631-6_106
  • Peer Reviewed
• [Presentation] Area bounds of rectilinear polygons realized by angle sequences (2012)
  • Author(s): Sang Won Bae, Yoshio Okamoto, and Chan-Su Shin
  • Organizer: 23rd International Symposium on Algorithms and Computation (ISAAC 2012)
  • Place of Presentation: National Taiwan University (台湾)
  • Year and Date: 2012-12-21
• [Presentation] Universal point subsets for planar graphs. (2012)
  • Author(s): Patrizio Angelini, Carla Binucci, William Evans, Ferran Hurtado Giuseppe Liotta Tamara Mchedlidze, Henk Meijer, and Yoshio Okamoto
  • Organizer: 23rd International Symposium on Algorithms and Computation (ISAAC 2012)
  • Place of Presentation: National Taiwan University (台湾)
  • Year and Date: 2012-12-20
• [Presentation] A4.31-approximation for the geometric unique coverage problem on unit disks (2012)
  • Author(s): Takehiro Ito, Shin-Ichi Nakano, Yoshio Okamoto, Yota Otachi, Ryuhei Uehara, Takeaki Uno, and Yushi Uno
  • Organizer: 23rd International Symposium onAlgorithms and Computation (ISAAC2012)
  • Place of Presentation: NationalTaiwan University (台湾)
  • Year and Date: 2012-12-20
• [Presentation] A polynomial-time approximation scheme for the geometric unique coverage problem on unit squares. (2012)
  • Author(s): Takehiro Ito, Shin-Ichi Nakano, Yoshio Okamoto, Yota Otachi, Ryuhei Uehara, Takeaki Uno, and Yushi Uno
  • Organizer: 13th Scandinavian Symposium and Workshop on Algorithm Theory (SWAT2012)
  • Place of Presentation: University ofHelsinki (フィンランド)
  • Year and Date: 2012-07-04
• [Presentation] On problems as hard as CNF-SAT (2012)
  • Author(s): Marek Cygan, Holger Dell, Daniel Lokshtanov, Daniel Marx, Jesper Nederlof, Yoshio Okamoto, Ramamohan Paturi, Saket Saurabh, and Magnus Wahlstrom
  • Organizer: 27th IEEE Conference on Computational Complexity (CCC 2012)
  • Place of Presentation: University of Porto (ポルトガル)
  • Year and Date: 2012-06-26
• [Presentation] Efficient enumeration of the directed binary perfect phylogenies from incomplete data (2012)
  • Author(s): Masashi Kiyomi, Yoshio Okamoto, and Toshiki Saitoh
  • Organizer: 11th International Symposium on Experimental Algorithms (SEA 2012)
  • Place of Presentation: LaBRi (フランス)
  • Year and Date: 2012-06-08
• [Presentation] Hardness results and an exact exponential algorithm for the spanning tree congestion problem (2011)
  • Author(s): Yoshio Okamoto, Yota Otachi, Ryuhei Uehara, and Takeaki Uno
  • Organizer: 8th Annual Conference on Theory and Applications of Models of Computation (TAMC 2011)
  • Place of Presentation: 電気通信大学(東京都)
  • Year and Date: 20110523-25
• [Presentation] Dominating set counting in graph classes (2011)
  • Author(s): Shuji Kijima, Yoshio Okamoto, and Takeaki Uno
  • Organizer: 17th Annual International Computing and Combinatorics Conference (COCOON2011)
  • Place of Presentation: Double Tree by Hilton Hotel Dallas-Richardson (アメリカ)
  • Year and Date: 2011-08-14
• [Presentation] Approximabilityof the path-distance-width for AT-free graphs (2011)
  • Author(s): Yota Otachi, Toshiki Saitoh, Katsuhisa Yamanaka, Shuji Kijima, Yoshio Okamoto, Hirotaka Ono, Yushi Uno, and Koichi Yamazaki
  • Organizer: 37th International Workshop on Graph-Theoretic Concepts in Computer Science (WG 2011)
  • Place of Presentation: Tepla Monastery (チェコ)
  • Year and Date: 2011-06-22
• [Presentation] Adaptive algorithms for planar convex hull problems (2010)
  • Author(s): Hee-Kap Ahn and Yoshio Okamoto
  • Organizer: 4th International Frontiers of Algorithmics Workshop (FAW 2010)
  • Place of Presentation: Wuhan Univeristy(中国)
  • Year and Date: 20100811-13
• [Presentation] The geodesic diameter of polygonal domains (2010)
  • Author(s): Sang Won Bae, Matias Korman, and Yoshio Okamoto
  • Organizer: 18th Annual European Symposium on Algorithms (ESA 2010)
  • Place of Presentation: Liverpool University (イギリス)
  • Year and Date: 2010-09-07
• [Presentation] Minimum and maximum against k lies (2010)
  • Author(s): Michael Hoffmann, Jiri Matousek, Yoshio Okamoto, and Philipp Zumstein
  • Organizer: 12th Scandinavian Symposium and Workshops on Algorithm Theory (SWAT 2010)
  • Place of Presentation: Studentsamskipnaden i Bergen (ノルウェー)
  • Year and Date: 2010-06-22
• [Presentation] Querying two boundary points for shortest paths in a polygonal domain (2009)
  • Author(s): Sang Won Bae and Yoshio Okamoto
  • Organizer: 20th International Symposium onAlgorithms and Computation (ISAAC2009)
  • Place of Presentation: Ala MoanaHotel (アメリカ)
  • Year and Date: 2009-12-18
• [Presentation] Counting the number of matchings in chordal and chordal bipartite graph classes (2009)
  • Author(s): Yoshio Okamoto, Ryuhei Uehara, and Takeaki Uno
  • Organizer: 35th International Workshop on Graph-Theoretic Concepts in Computer Science (WG 2009)
  • Place of Presentation: Montpellier (フランス)
  • Year and Date: 2009-06-26
• [Book] 離散数学のすすめ (2010)
  • Author(s): 伊藤大雄,宇野裕之(編著),岡本吉央,他21名(共著)
  • Total Pages: 48-57
  • Publisher: 現代数学社
• [Book] 「離散体積計算から見た組合せ数学入門」 (2010)
  • Author(s): M.ベック,S.ロビンス(著),岡本吉央(訳)
  • Total Pages: 267
  • Publisher: シュプリンガー・ジャパン