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(n 2) operations. Thus the presently known best algorithms are optimal to within a multiplicative constant.
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Holt, R.C., Reingold, E.M. On the time required to detect cycles and connectivity in graphs. Math. Systems Theory 6, 103–106 (1972). https://doi.org/10.1007/BF01706081
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DOI: https://doi.org/10.1007/BF01706081