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Listing Induced Steiner Subgraphs as a Compact Way to Discover Steiner Trees in Graphs

Authors Alessio Conte, Roberto Grossi, Mamadou Moustapha Kanté, Andrea Marino, Takeaki Uno, Kunihiro Wasa

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Author Details

Alessio Conte
  • Dipartimento di Informatica, Università di Pisa, Italy
Roberto Grossi
  • Dipartimento di Informatica, Università di Pisa, Italy
Mamadou Moustapha Kanté
  • Université Clermont Auvergne, LIMOS, CNRS, Aubière, France
Andrea Marino
  • Dipartimento di Statistica, Informatica, Applicazioni, Università di Firenze, Italy
Takeaki Uno
  • National Institute of Informatics, Tokyo, Japan
Kunihiro Wasa
  • National Institute of Informatics, Tokyo, Japan

Funding

This work was partially supported by JST CREST grant number JPMJCR1401 and JPMJCR18K3 Japan, by JSPS KAKENHI Grant Number JP19K20350 Japan, and by MIUR, Italy. Mamadou M. Kanté is supported by French Agency for Research under the GraphEN project (ANR-15-CE40-0009).

Cite AsGet BibTex

Alessio Conte, Roberto Grossi, Mamadou Moustapha Kanté, Andrea Marino, Takeaki Uno, and Kunihiro Wasa. Listing Induced Steiner Subgraphs as a Compact Way to Discover Steiner Trees in Graphs. In 44th International Symposium on Mathematical Foundations of Computer Science (MFCS 2019). Leibniz International Proceedings in Informatics (LIPIcs), Volume 138, pp. 73:1-73:14, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2019)
https://doi.org/10.4230/LIPIcs.MFCS.2019.73

Abstract

This paper investigates induced Steiner subgraphs as a variant of the classical Steiner trees, so as to compactly represent the (exponentially many) Steiner trees sharing the same underlying induced subgraph. We prove that the enumeration of all (inclusion-minimal) induced Steiner subgraphs is harder than the well-known Hypergraph Transversal enumeration problem if the number of terminals is not fixed. When the number of terminals is fixed, we propose a polynomial delay algorithm for listing all induced Steiner subgraphs of minimum size. We also propose a polynomial delay algorithm for listing the set of minimal induced Steiner subgraphs when the number of terminals is 3.

Subject Classification

ACM Subject Classification
  • Mathematics of computing → Graph enumeration
Keywords
  • Graph algorithms
  • enumeration
  • listing and counting
  • Steiner trees
  • induced subgraphs

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References

  1. A. Aazami, J. Cheriyan, and K. R. Jampani. Approximation Algorithms and Hardness Results for Packing Element-Disjoint Steiner Trees in Planar Graphs. Algorithmica, 63(1-2):425-456, June 2012. Google Scholar
  2. Lijun Chang, Xuemin Lin, Lu Qin, Jeffrey Xu Yu, and Wenjie Zhang. Index-based Optimal Algorithms for Computing Steiner Components with Maximum Connectivity. In Proceedings of the 2015 ACM SIGMOD International Conference on Management of Data, SIGMOD '15, pages 459-474, New York, NY, USA, 2015. ACM. URL: https://doi.org/10.1145/2723372.2746486.
  3. Chandra Chekuri, Alina Ene, and Ali Vakilian. Node-Weighted Network Design in Planar and Minor-Closed Families of Graphs. In Artur Czumaj, Kurt Mehlhorn, Andrew M. Pitts, and Roger Wattenhofer, editors, Automata, Languages, and Programming - 39th International Colloquium, ICALP 2012, Warwick, UK, July 9-13, 2012, Proceedings, Part I, volume 7391 of Lecture Notes in Computer Science, pages 206-217. Springer, 2012. Google Scholar
  4. Joseph Cheriyan and Mohammad R. Salavatipour. Packing element-disjoint Steiner trees. ACM Transactions on Algorithms, 3(4):47:1-47:10, November 2007. URL: https://doi.org/10.1145/1290672.1290684.
  5. Alessio Conte, Roberto Grossi, Andrea Marino, Takeaki Uno, and Luca Versari. Listing Maximal Independent Sets with Minimal Space and Bounded Delay. In String Processing and Information Retrieval - 24th International Symposium, SPIRE 2017, Palermo, Italy, September 26-29, 2017, Proceedings, pages 144-160, 2017. URL: https://doi.org/10.1007/978-3-319-67428-5_13.
  6. Nicolas Derhy and Christophe Picouleau. Finding induced trees. Discrete Applied Mathematics, 157(17):3552-3557, 2009. Google Scholar
  7. Reinhard Diestel. Graph Theory, 4th Edition, volume 173 of Graduate texts in mathematics. Springer, 2012. Google Scholar
  8. DIMACS. 11th DIMACS Implementation Challenge. http://dimacs11.zib.de/, 2014 (page accessed April 2019).
  9. Mitre C. Dourado, Rodolfo A. Oliveira, and Fábio Protti. Algorithmic aspects of Steiner convexity and enumeration of Steiner trees. Annals of Operations Research, 223(1):155-171, December 2014. URL: https://doi.org/10.1007/s10479-014-1607-5.
  10. Thomas Eiter, Kazuhisa Makino, and Georg Gottlob. Computational Aspects of Monotone Dualization: A Brief Survey. Discrete Appl. Math., 156(11):2035-2049, June 2008. Google Scholar
  11. Sudipto Guha and Samir Khuller. Improved Methods for Approximating Node Weighted Steiner Trees and Connected Dominating Sets. Information and Computation, 150(1):57-74, 1999. URL: https://doi.org/10.1006/inco.1998.2754.
  12. Mathias Hauptmann and Marek Karpinski. A Compendium on Steiner Tree Problems. http://theory.cs.uni-bonn.de/info5/steinerkompendium/, Accessed February 2018.
  13. Daiki Hoshika and Eiji Miyano. Approximation Algorithms for Packing Element-Disjoint Steiner Trees on Bounded Terminal Nodes. IEICE Transactions, 99-A(6):1059-1066, 2016. URL: http://search.ieice.org/bin/summary.php?id=e99-a_6_1059.
  14. Jiafeng Hu, Xiaowei Wu, Reynold Cheng, Siqiang Luo, and Yixiang Fang. On Minimal Steiner Maximum-Connected Subgraph Queries. IEEE Trans. Knowl. Data Eng, 29(11):2455-2469, 2017. URL: https://doi.org/10.1109/TKDE.2017.2730873.
  15. L. Khachiyan, E. Boros, K. Elbassioni, V. Gurvich, and K. Makino. On the Complexity of Some Enumeration Problems for Matroids. SIAM Journal on Discrete Mathematics, 19(4):966-984, January 2005. URL: https://doi.org/10.1137/S0895480103428338.
  16. PACE. The parametrized Algorithms and Computational Experiments Challenge. https://pacechallenge.wordpress.com/pace-2018/, 2018.
  17. Jan Arne Telle and Yngve Villanger. Connecting Terminals and 2-Disjoint Connected Subgraphs. In Graph-Theoretic Concepts in Computer Science, pages 418-428. Springer Berlin Heidelberg, 2013. Google Scholar
  18. Takeaki Uno. An Output Linear Time Algorithm for Enumerating Chordless Cycles. IPSJ SIG Notes, 2003(110):47-53, November 2003. Google Scholar
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