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标题：Enumeration of s-d Separators in DAGs with Application to Reliability Analysis in Temporal Graphs
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作者：Alessio Conte ; Pierluigi Crescenzi ; Andrea Marino 等
期刊名称：LIPIcs : Leibniz International Proceedings in Informatics
电子版ISSN：1868-8969
出版年度：2020
卷号：170
页码：25:1-25:14
DOI：10.4230/LIPIcs.MFCS.2020.25
出版社：Schloss Dagstuhl -- Leibniz-Zentrum fuer Informatik
摘要：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(mÂ³), where m is the number of temporal arcs.
关键词：minimal cutset; temporal graph; minimal separator; directed acyclic graph