Conte, Alessio
[VerfasserIn];
Crescenzi, Pierluigi
[VerfasserIn];
Marino, Andrea
[VerfasserIn];
Punzi, Giulia
[VerfasserIn]
;
Alessio Conte and Pierluigi Crescenzi and Andrea Marino and Giulia Punzi
[MitwirkendeR]
Enumeration of s-d Separators in DAGs with Application to Reliability Analysis in Temporal Graphs
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Beschreibung:
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.