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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).

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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

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