Finding Minimum Cutsets in Reducible Graphs

Abstract

The analysis of many processes modelled by directed graphs requires the selection of a subset of vertices which cut all the cycles in the graph. Reducing the size of such a cutset usually leads to a simpler and more efficient analysis, but the problem of finding minimum cutsets in general directed graphs is know to be NP-complete. In this paper we show that in reducible graphs (and thus in almost all the "practicla" flowcahrts of programs), minimum cutsets can be found in linear time. An immediate application of this result is in program verification systems based on Floyd's inductive assertions method.