Reconfiguration of Minimum Steiner Trees via Vertex Exchanges

Authors Haruka Mizuta, Tatsuhiko Hatanaka, Takehiro Ito , Xiao Zhou

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Haruka Mizuta
  • Graduate School of Information Sciences, Tohoku University, Sendai, Japan
Tatsuhiko Hatanaka
  • Graduate School of Information Sciences, Tohoku University, Sendai, Japan
Takehiro Ito
  • Graduate School of Information Sciences, Tohoku University, Sendai, Japan
Xiao Zhou
  • Graduate School of Information Sciences, Tohoku University, Sendai, Japan

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Haruka Mizuta, Tatsuhiko Hatanaka, Takehiro Ito, and Xiao Zhou. Reconfiguration of Minimum Steiner Trees via Vertex Exchanges. In 44th International Symposium on Mathematical Foundations of Computer Science (MFCS 2019). Leibniz International Proceedings in Informatics (LIPIcs), Volume 138, pp. 79:1-79:11, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2019)


In this paper, we study the problem of deciding if there is a transformation between two given minimum Steiner trees of an unweighted graph such that each transformation step respects a prescribed reconfiguration rule and results in another minimum Steiner tree of the graph. We consider two reconfiguration rules, both of which exchange a single vertex at a time, and generalize the known reconfiguration problem for shortest paths in an unweighted graph. This generalization implies that our problems under both reconfiguration rules are PSPACE-complete for bipartite graphs. We thus study the problems with respect to graph classes, and give some boundaries between the polynomial-time solvable and PSPACE-complete cases.

Subject Classification

ACM Subject Classification
  • Mathematics of computing → Graph algorithms
  • Combinatorial reconfiguration
  • Graph algorithms
  • Steiner tree


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