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DOI: 10.4230/LIPIcs.MFCS.2020.25
URN: urn:nbn:de:0030-drops-126932
URL: https://drops.dagstuhl.de/opus/volltexte/2020/12693/
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 | |
| Seminar: | 45th International Symposium on Mathematical Foundations of Computer Science (MFCS 2020) | |
| Issue date: | 2020 | |
| Date of publication: | 18.08.2020 |
