An algorithm for generation of s‐t acyclic graphs

Abstract

AbstractThe problem of finding all s‐t acyclic graphs between two given vertices of a digraph is interesting in relation to the evaluation of the reliability of a communication network. There is already an algorithm which generates all s‐t acyclic digraphs without duplication by opening an arc or a set of arcs one by one starting with a given graph. But the efficiency of that algorithm decreases when the number of cycles in the graph becomes large. This paper proposes an algorithm which generates s‐t acyclic graphs without duplication by combining s‐t paths obtained by a depth‐first search. Compared with the existing algorithms (i) the execution time of this algorithm is not affected much by the number of arc disjoint cycles of the graph; (ii) when the generation is stopped at an arbitrary level i, all the s‐t acyclic graphs composed of paths of length i or less will have been generated. Thus they can be used to approximate the reliability.