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

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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)


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
  • Graph algorithms
  • enumeration
  • listing and counting
  • Steiner trees
  • induced subgraphs


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