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DOI: 10.4230/LIPIcs.MFCS.2023.50

An FPT Algorithm for Spanning Trees with Few Branch Vertices Parameterized by Modular-Width

Authors: Luisa Gargano and Adele A. Rescigno

Published in: LIPIcs, Volume 272, 48th International Symposium on Mathematical Foundations of Computer Science (MFCS 2023)

Abstract

The minimum branch vertices spanning tree problem consists in finding a spanning tree T of an input graph G having the minimum number of branch vertices, that is, vertices of degree at least three in T. This NP-hard problem has been widely studied in the literature and has many important applications in network design and optimization. Algorithmic and combinatorial aspects of the problem have been extensively studied and its fixed parameter tractability has been recently considered. In this paper we focus on modular-width and show that the problem of finding a spanning tree with the minimum number of branch vertices is FPT with respect to this parameter.

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Luisa Gargano and Adele A. Rescigno. An FPT Algorithm for Spanning Trees with Few Branch Vertices Parameterized by Modular-Width. In 48th International Symposium on Mathematical Foundations of Computer Science (MFCS 2023). Leibniz International Proceedings in Informatics (LIPIcs), Volume 272, pp. 50:1-50:15, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2023)

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@InProceedings{gargano_et_al:LIPIcs.MFCS.2023.50,
  author =	{Gargano, Luisa and Rescigno, Adele A.},
  title =	{{An FPT Algorithm for Spanning Trees with Few Branch Vertices Parameterized by Modular-Width}},
  booktitle =	{48th International Symposium on Mathematical Foundations of Computer Science (MFCS 2023)},
  pages =	{50:1--50:15},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-292-1},
  ISSN =	{1868-8969},
  year =	{2023},
  volume =	{272},
  editor =	{Leroux, J\'{e}r\^{o}me and Lombardy, Sylvain and Peleg, David},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.MFCS.2023.50},
  URN =		{urn:nbn:de:0030-drops-185843},
  doi =		{10.4230/LIPIcs.MFCS.2023.50},
  annote =	{Keywords: Spanning Trees, Branch vertices, Fixed-parameter tractable algorithms, Modular-width}
}

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DOI: 10.4230/LIPIcs.FUN.2021.21

Speeding up Networks Mining via Neighborhood Diversity

Authors: Gennaro Cordasco, Luisa Gargano, and Adele A. Rescigno

Published in: LIPIcs, Volume 157, 10th International Conference on Fun with Algorithms (FUN 2021) (2020)

Abstract

Parameterized complexity was classically used to efficiently solve NP-hard problems for small values of a fixed parameter. Then it has also been used as a tool to speed up algorithms for tractable problems. Following this line of research, we design algorithms parameterized by neighborhood diversity (nd) for several graph theoretic problems in P (e.g., Maximum Matching, Triangle counting and listing, Girth and Global minimum vertex cut). Such problems are known to admit algorithms parameterized by modular-width (mw) and consequently - being the nd a "special case" of mw - by nd. However, the proposed novel algorithms allow to improve the computational complexity from a time O(f(mw)⋅ n +m) - where n and m denote, respectively, the number of vertices and edges in the input graph - which is multiplicative in n to a time O(g(nd)+n +m) which is additive only in the size of the input.

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Gennaro Cordasco, Luisa Gargano, and Adele A. Rescigno. Speeding up Networks Mining via Neighborhood Diversity. In 10th International Conference on Fun with Algorithms (FUN 2021). Leibniz International Proceedings in Informatics (LIPIcs), Volume 157, pp. 21:1-21:12, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2020)

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@InProceedings{cordasco_et_al:LIPIcs.FUN.2021.21,
  author =	{Cordasco, Gennaro and Gargano, Luisa and Rescigno, Adele A.},
  title =	{{Speeding up Networks Mining via Neighborhood Diversity}},
  booktitle =	{10th International Conference on Fun with Algorithms (FUN 2021)},
  pages =	{21:1--21:12},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-145-0},
  ISSN =	{1868-8969},
  year =	{2020},
  volume =	{157},
  editor =	{Farach-Colton, Martin and Prencipe, Giuseppe and Uehara, Ryuhei},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.FUN.2021.21},
  URN =		{urn:nbn:de:0030-drops-127823},
  doi =		{10.4230/LIPIcs.FUN.2021.21},
  annote =	{Keywords: Parameterized Complexity, Neighborhood Diversity, Maximum Matching, Triangle Counting, Girth, Global minimum vertex cut}
}

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Documents authored by Rescigno, Adele A.

An FPT Algorithm for Spanning Trees with Few Branch Vertices Parameterized by Modular-Width

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Speeding up Networks Mining via Neighborhood Diversity

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