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.
@InProceedings{conte_et_al:LIPIcs.MFCS.2019.73, author = {Conte, Alessio and Grossi, Roberto and Kant\'{e}, Mamadou Moustapha and Marino, Andrea and Uno, Takeaki and Wasa, Kunihiro}, title = {{Listing Induced Steiner Subgraphs as a Compact Way to Discover Steiner Trees in Graphs}}, booktitle = {44th International Symposium on Mathematical Foundations of Computer Science (MFCS 2019)}, pages = {73:1--73:14}, series = {Leibniz International Proceedings in Informatics (LIPIcs)}, ISBN = {978-3-95977-117-7}, ISSN = {1868-8969}, year = {2019}, volume = {138}, editor = {Rossmanith, Peter and Heggernes, Pinar and Katoen, Joost-Pieter}, publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik}, address = {Dagstuhl, Germany}, URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.MFCS.2019.73}, URN = {urn:nbn:de:0030-drops-110174}, doi = {10.4230/LIPIcs.MFCS.2019.73}, annote = {Keywords: Graph algorithms, enumeration, listing and counting, Steiner trees, induced subgraphs} }
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