License: Creative Commons Attribution 4.0 International license (CC BY 4.0)
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DOI: 10.4230/LIPIcs.MFCS.2022.78
URN: urn:nbn:de:0030-drops-168769
URL: http://dagstuhl.sunsite.rwth-aachen.de/volltexte/2022/16876/
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Ramanujan, M. S. ; Sahu, Abhishek ; Saurabh, Saket ; Verma, Shaily

An Exact Algorithm for Knot-Free Vertex Deletion

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LIPIcs-MFCS-2022-78.pdf (0.8 MB)

Abstract

The study of the Knot-Free Vertex Deletion problem emerges from its application in the resolution of deadlocks called knots, detected in a classical distributed computation model, that is, the OR-model. A strongly connected subgraph Q of a digraph D with at least two vertices is said to be a knot if there is no arc (u,v) of D with u ∈ V(Q) and v ∉ V(Q) (no-out neighbors of the vertices in Q). Given a directed graph D, the Knot-Free Vertex Deletion (KFVD) problem asks to compute a minimum-size subset S ⊂ V(D) such that D[V⧵S] contains no knots. There is no exact algorithm known for the KFVD problem in the literature that is faster than the trivial O^⋆(2ⁿ) brute-force algorithm. In this paper, we obtain the first non-trivial upper bound for KFVD by designing an exact algorithm running in time ?^⋆(1.576ⁿ), where n is the size of the vertex set in D.

BibTeX - Entry

@InProceedings{ramanujan_et_al:LIPIcs.MFCS.2022.78,
  author =	{Ramanujan, M. S. and Sahu, Abhishek and Saurabh, Saket and Verma, Shaily},
  title =	{{An Exact Algorithm for Knot-Free Vertex Deletion}},
  booktitle =	{47th International Symposium on Mathematical Foundations of Computer Science (MFCS 2022)},
  pages =	{78:1--78:15},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-256-3},
  ISSN =	{1868-8969},
  year =	{2022},
  volume =	{241},
  editor =	{Szeider, Stefan and Ganian, Robert and Silva, Alexandra},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/opus/volltexte/2022/16876},
  URN =		{urn:nbn:de:0030-drops-168769},
  doi =		{10.4230/LIPIcs.MFCS.2022.78},
  annote =	{Keywords: exact algorithm, knot-free graphs, branching algorithm}
}

Keywords: exact algorithm, knot-free graphs, branching algorithm
Collection: 47th International Symposium on Mathematical Foundations of Computer Science (MFCS 2022)
Issue Date: 2022
Date of publication: 22.08.2022

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