Abstract
We present an algorithm which can find a negative cycle in a directed graph in worst case time O(n·e), where n is the number of nodes and e the number of edges, using only space O(n + e). Our algorithm is implemented on a pointer machine. Assuming that the input to our algorithm is a weighted random digraph, we prove that its average time complexity for dense graphs lies between O(n·logn) and O(min{n 2/log 2 n,e}), the exact value depending on the probability with which an edge is present in the random graph, and for sparse random graphs is Θ(n 2).
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© 1986 Springer-Verlag Berlin Heidelberg
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Spirakis, P., Tsakalidis, A. (1986). A very fast, practical algorithm for finding a negative cycle in a digraph. In: Kott, L. (eds) Automata, Languages and Programming. ICALP 1986. Lecture Notes in Computer Science, vol 226. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-16761-7_89
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DOI: https://doi.org/10.1007/3-540-16761-7_89
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