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

Authors Alessio Conte, Pierluigi Crescenzi, Andrea Marino, Giulia Punzi

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Subject Classification

ACM Subject Classification
  • Theory of computation → Graph algorithms analysis
Keywords
  • minimal cutset
  • temporal graph
  • minimal separator
  • directed acyclic graph

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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.

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Alessio Conte, Pierluigi Crescenzi, Andrea Marino, and Giulia Punzi. Enumeration of s-d Separators in DAGs with Application to Reliability Analysis in Temporal Graphs. In 45th International Symposium on Mathematical Foundations of Computer Science (MFCS 2020). Leibniz International Proceedings in Informatics (LIPIcs), Volume 170, pp. 25:1-25:14, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2020) https://doi.org/10.4230/LIPIcs.MFCS.2020.25

Author Details

Alessio Conte
  • Università degli Studi di Pisa, Dipartimento di Informatica, Italy
Pierluigi Crescenzi
  • Université de Paris, IRIF, CNRS, France
  • On-leave from Università degli Studi di Firenze, DiMaI, Firenze, Italy
Andrea Marino
  • Università degli Studi di Firenze, DiSIA, Firenze, Italy
Giulia Punzi
  • Università degli Studi di Pisa, Dipartimento di Informatica, Italy

Funding

A.C. and A.M. have been partially supported by MIUR under PRIN Project AHeAD (Efficient Algorithms for HArnessing Networked Data). A.M. has been partially supported by University of Florence under Project GRANTED (GRaph Algorithms for Networked TEmporal Data).

Acknowledgements

We would like to thank Gaurav Khanna and Lhouari Nourine for several useful discussion by e-mail.

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