License: Creative Commons Attribution 3.0 Unported license (CC BY 3.0)
When quoting this document, please refer to the following
DOI: 10.4230/LIPIcs.MFCS.2020.25
URN: urn:nbn:de:0030-drops-126932
URL: http://dagstuhl.sunsite.rwth-aachen.de/volltexte/2020/12693/
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Conte, Alessio ; Crescenzi, Pierluigi ; Marino, Andrea ; Punzi, Giulia

Enumeration of s-d Separators in DAGs with Application to Reliability Analysis in Temporal Graphs

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Abstract

Temporal graphs are graphs in which arcs have temporal labels, specifying at which time they can be traversed. Motivated by recent results concerning the reliability analysis of a temporal graph through the enumeration of minimal cutsets in the corresponding line graph, in this paper we attack the problem of enumerating minimal s-d separators in s-d directed acyclic graphs (in short, s-d DAGs), also known as 2-terminal DAGs or s-t digraphs. Our main result is an algorithm for enumerating all the minimal s-d separators in a DAG with O(nm) delay, where n and m are respectively the number of nodes and arcs, and the delay is the time between the output of two consecutive solutions. To this aim, we give a characterization of the minimal s-d separators in a DAG through vertex cuts of an expanded version of the DAG itself. As a consequence of our main result, we provide an algorithm for enumerating all the minimal s-d cutsets in a temporal graph with delay O(m³), where m is the number of temporal arcs.

BibTeX - Entry

@InProceedings{conte_et_al:LIPIcs:2020:12693,
  author =	{Alessio Conte and Pierluigi Crescenzi and Andrea Marino and Giulia Punzi},
  title =	{{Enumeration of s-d Separators in DAGs with Application to Reliability Analysis in Temporal Graphs}},
  booktitle =	{45th International Symposium on Mathematical Foundations of Computer Science (MFCS 2020)},
  pages =	{25:1--25:14},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-159-7},
  ISSN =	{1868-8969},
  year =	{2020},
  volume =	{170},
  editor =	{Javier Esparza and Daniel Kr{\'a}ľ},
  publisher =	{Schloss Dagstuhl--Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/opus/volltexte/2020/12693},
  URN =		{urn:nbn:de:0030-drops-126932},
  doi =		{10.4230/LIPIcs.MFCS.2020.25},
  annote =	{Keywords: minimal cutset, temporal graph, minimal separator, directed acyclic graph}
}

Keywords: minimal cutset, temporal graph, minimal separator, directed acyclic graph
Collection: 45th International Symposium on Mathematical Foundations of Computer Science (MFCS 2020)
Issue Date: 2020
Date of publication: 18.08.2020

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