On the Time Required to Detect Cycles and Connectivity in Directed Graphs (original) (raw)

1970

Abstract

ABSTRACT It is shown that when a graph is represented as a binary connection matrix, the problems of finding the shortest path between two nodes of a graph, of determining whether the graph has a cycle, and of determining if a graph is strongly connected each require at leastO(n2) operations. Thus the presently known best algorithms are optimal to within a multiplicative constant.

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