Document Open Access Logo

Enumerating All Subgraphs Under Given Constraints Using Zero-Suppressed Sentential Decision Diagrams

Authors Yu Nakahata , Masaaki Nishino , Jun Kawahara , Shin-ichi Minato

PDF
Thumbnail PDF

File

LIPIcs.SEA.2020.9.pdf
  • Filesize: 1.05 MB
  • 14 pages

Document Identifiers

Author Details

Yu Nakahata
  • Graduate School of Informatics, Kyoto University, Japan
Masaaki Nishino
  • NTT Communication Science Laboratories, NTT Corporation, Kyoto, Japan
Jun Kawahara
  • Graduate School of Informatics, Kyoto University, Japan
Shin-ichi Minato
  • Graduate School of Informatics, Kyoto University, Japan

Funding

This work was supported by JSPS KAKENHI Grant Number JP15H05711, JP18H04091, JP18K04610, and JP19J21000.

Cite AsGet BibTex

Yu Nakahata, Masaaki Nishino, Jun Kawahara, and Shin-ichi Minato. Enumerating All Subgraphs Under Given Constraints Using Zero-Suppressed Sentential Decision Diagrams. In 18th International Symposium on Experimental Algorithms (SEA 2020). Leibniz International Proceedings in Informatics (LIPIcs), Volume 160, pp. 9:1-9:14, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2020)
https://doi.org/10.4230/LIPIcs.SEA.2020.9

Abstract

Subgraph enumeration is a fundamental task in computer science. Since the number of subgraphs can be large, some enumeration algorithms exploit compressed representations for efficiency. One such representation is the Zero-suppressed Binary Decision Diagram (ZDD). ZDDs can represent the set of subgraphs compactly and support several poly-time queries, such as counting and random sampling. Researchers have proposed efficient algorithms to construct ZDDs representing the set of subgraphs under several constraints, which yield fruitful results in many applications. Recently, Zero-suppressed Sentential Decision Diagrams (ZSDDs) have been proposed as variants of ZDDs. ZSDDs can be smaller than ZDDs when representing the same set of subgraphs. However, efficient algorithms to construct ZSDDs are known only for specific types of subgraphs: matchings and paths. We propose a novel framework to construct ZSDDs representing sets of subgraphs under given constraints. Using our framework, we can construct ZSDDs representing several sets of subgraphs such as matchings, paths, cycles, and spanning trees. We show the bound of sizes of constructed ZSDDs by the branch-width of the input graph, which is smaller than that of ZDDs by the path-width. Experiments show that our methods can construct ZSDDs faster than ZDDs and that the constructed ZSDDs are smaller than ZDDs when representing the same set of subgraphs.

Subject Classification

ACM Subject Classification
  • Mathematics of computing → Graph algorithms
Keywords
  • Subgraph
  • Enumeration
  • Decision Diagram
  • Zero-suppressed Sentential Decision Diagram (ZSDD)
  • Top-down construction algorithm

Metrics

  • Access Statistics
  • Total Accesses (updated on a weekly basis)
    0
    PDF Downloads
    0
    Metadata Views

References

  1. Etienne Birmelé, Rui A. Ferreira, Roberto Grossi, Andrea Marino, Nadia Pisanti, Romeo Rizzi, and Gustavo Sacomoto. Optimal listing of cycles and st-paths in undirected graphs. In Sanjeev Khanna, editor, Proceedings of the Twenty-Fourth Annual ACM-SIAM Symposium on Discrete Algorithms, SODA 2013, New Orleans, Louisiana, USA, January 6-8, 2013, pages 1884-1896. SIAM, 2013. URL: https://doi.org/10.1137/1.9781611973105.134.
  2. Hans L. Bodlaender. A partial k-arboretum of graphs with bounded treewidth. Theor. Comput. Sci., 209(1-2):1-45, 1998. URL: https://doi.org/10.1016/S0304-3975(97)00228-4.
  3. Simone Bova. Sdds are exponentially more succinct than obdds. In Dale Schuurmans and Michael P. Wellman, editors, Proceedings of the Thirtieth AAAI Conference on Artificial Intelligence, February 12-17, 2016, Phoenix, Arizona, USA, pages 929-935. AAAI Press, 2016. URL: http://www.aaai.org/ocs/index.php/AAAI/AAAI16/paper/view/12270.
  4. Randal E. Bryant. Graph-based algorithms for boolean function manipulation. IEEE Trans. Computers, 35(8):677-691, 1986. URL: https://doi.org/10.1109/TC.1986.1676819.
  5. Alessio Conte, Roberto Grossi, Andrea Marino, and Luca Versari. Sublinear-space bounded-delay enumeration for massive network analytics: Maximal cliques. In Ioannis Chatzigiannakis, Michael Mitzenmacher, Yuval Rabani, and Davide Sangiorgi, editors, 43rd International Colloquium on Automata, Languages, and Programming, ICALP 2016, July 11-15, 2016, Rome, Italy, volume 55 of LIPIcs, pages 148:1-148:15. Schloss Dagstuhl - Leibniz-Zentrum für Informatik, 2016. URL: https://doi.org/10.4230/LIPIcs.ICALP.2016.148.
  6. William J. Cook and Paul D. Seymour. Tour merging via branch-decomposition. INFORMS J. Comput., 15(3):233-248, 2003. URL: https://doi.org/10.1287/ijoc.15.3.233.16078.
  7. Gary Hardy, Corinne Lucet, and Nikolaos Limnios. K-terminal network reliability measures with binary decision diagrams. IEEE Trans. Reliability, 56(3):506-515, 2007. URL: https://doi.org/10.1109/TR.2007.898572.
  8. Hiroshi Imai, Kyoko Sekine, and Keiko Imai. Computational investigations of all-terminal network reliability via BDDs. IEICE Transactions on Fundamentals of Electronics, Communications and Computer Sciences, E82-A:714-721, 1999. Google Scholar
  9. Takeru Inoue, Hiroaki Iwashita, Jun Kawahara, and Shin-ichi Minato. Graphillion: software library for very large sets of labeled graphs. Int. J. Softw. Tools Technol. Transf., 18(1):57-66, 2016. URL: https://doi.org/10.1007/s10009-014-0352-z.
  10. Takeru Inoue, Keiji Takano, Takayuki Watanabe, Jun Kawahara, Ryo Yoshinaka, Akihiro Kishimoto, Koji Tsuda, Shin-ichi Minato, and Yasuhiro Hayashi. Distribution loss minimization with guaranteed error bound. IEEE Trans. Smart Grid, 5(1):102-111, 2014. URL: https://doi.org/10.1109/TSG.2013.2288976.
  11. Yuma Inoue and Shin-ichi Minato. Acceleration of ZDD construction for subgraph enumeration via path-width optimization. TCS-TR-A-16-80. Hokkaido University, 2016. Google Scholar
  12. Jun Kawahara, Takashi Horiyama, Keisuke Hotta, and Shin-ichi Minato. Generating all patterns of graph partitions within a disparity bound. In Sheung-Hung Poon, Md. Saidur Rahman, and Hsu-Chun Yen, editors, WALCOM: Algorithms and Computation, 11th International Conference and Workshops, WALCOM 2017, Hsinchu, Taiwan, March 29-31, 2017, Proceedings, volume 10167 of Lecture Notes in Computer Science, pages 119-131. Springer, 2017. URL: https://doi.org/10.1007/978-3-319-53925-6_10.
  13. Jun Kawahara, Takeru Inoue, Hiroaki Iwashita, and Shin-ichi Minato. Frontier-based search for enumerating all constrained subgraphs with compressed representation. IEICE Transactions on Fundamentals of Electronics, Communications and Computer Sciences, E100-A(9):1773-1784, 2017. Google Scholar
  14. Donald E. Knuth. The art of computer programming, Vol. 4A, Combinatorial algorithms, Part 1. Addison-Wesley Professional, 1st edition, 2011. Google Scholar
  15. Shin-ichi Minato. Zero-suppressed bdds for set manipulation in combinatorial problems. In Alfred E. Dunlop, editor, Proceedings of the 30th Design Automation Conference. Dallas, Texas, USA, June 14-18, 1993, pages 272-277. ACM Press, 1993. URL: https://doi.org/10.1145/157485.164890.
  16. Yu Nakahata, Jun Kawahara, Takashi Horiyama, and Shoji Kasahara. Enumerating all spanning shortest path forests with distance and capacity constraints. IEICE Transactions on Fundamentals of Electronics, Communications and Computer Sciences, E101-A(9):1363-1374, 2018. Google Scholar
  17. Yu Nakahata, Jun Kawahara, and Shoji Kasahara. Enumerating graph partitions without too small connected components using zero-suppressed binary and ternary decision diagrams. In Gianlorenzo D'Angelo, editor, 17th International Symposium on Experimental Algorithms, SEA 2018, June 27-29, 2018, L'Aquila, Italy, volume 103 of LIPIcs, pages 21:1-21:13. Schloss Dagstuhl - Leibniz-Zentrum für Informatik, 2018. URL: https://doi.org/10.4230/LIPIcs.SEA.2018.21.
  18. Masaaki Nishino, Norihito Yasuda, Shin-ichi Minato, and Masaaki Nagata. Zero-suppressed sentential decision diagrams. In Dale Schuurmans and Michael P. Wellman, editors, Proceedings of the Thirtieth AAAI Conference on Artificial Intelligence, February 12-17, 2016, Phoenix, Arizona, USA, pages 1058-1066. AAAI Press, 2016. URL: http://www.aaai.org/ocs/index.php/AAAI/AAAI16/paper/view/12434.
  19. Masaaki Nishino, Norihito Yasuda, Shin-ichi Minato, and Masaaki Nagata. Compiling graph substructures into sentential decision diagrams. In Satinder P. Singh and Shaul Markovitch, editors, Proceedings of the Thirty-First AAAI Conference on Artificial Intelligence, February 4-9, 2017, San Francisco, California, USA, pages 1213-1221. AAAI Press, 2017. URL: http://aaai.org/ocs/index.php/AAAI/AAAI17/paper/view/14919.
  20. Kyoko Sekine, Hiroshi Imai, and Seiichiro Tani. Computing the tutte polynomial of a graph of moderate size. In John Staples, Peter Eades, Naoki Katoh, and Alistair Moffat, editors, Algorithms and Computation, 6th International Symposium, ISAAC '95, Cairns, Australia, December 4-6, 1995, Proceedings, volume 1004 of Lecture Notes in Computer Science, pages 224-233. Springer, 1995. URL: https://doi.org/10.1007/BFb0015427.
  21. Akiyoshi Shioura, Akihisa Tamura, and Takeaki Uno. An optimal algorithm for scanning all spanning trees of undirected graphs. SIAM J. Comput., 26(3):678-692, 1997. URL: https://doi.org/10.1137/S0097539794270881.
  22. Yexiang Xue, Arthur Choi, and Adnan Darwiche. Basing decisions on sentences in decision diagrams. In Jörg Hoffmann and Bart Selman, editors, Proceedings of the Twenty-Sixth AAAI Conference on Artificial Intelligence, July 22-26, 2012, Toronto, Ontario, Canada. AAAI Press, 2012. URL: http://www.aaai.org/ocs/index.php/AAAI/AAAI12/paper/view/4977.
Questions / Remarks / Feedback
X

Feedback for Dagstuhl Publishing


Thanks for your feedback!

Feedback submitted

Could not send message

Please try again later or send an E-mail
© 2023-2024 Schloss Dagstuhl – LZI GmbH Imprint Privacy Contact