Abstract
We study the problem of finding a negative length cycle in a network. An algorithm for the negative cycle problem combines a shortest path algorithm and a cycle detection strategy. We study various combinations of shortest path algorithms and cycle detection strategies and find the best combinations. One of our discoveries is that a cycle detection strategy of Tarjan greatly improves practical performance of a classical shortest path algorithm, making it competitive with the fastest known algorithms on a wide range of problems. As a part of our study, we develop problem families for testing negative cycle algorithms.
This work was done while the first author was visiting NEC Research Institute, Inc.
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Cherkassky, B.V., Goldberg, A.V. (1996). Negative-cycle detection algorithms. In: Diaz, J., Serna, M. (eds) Algorithms — ESA '96. ESA 1996. Lecture Notes in Computer Science, vol 1136. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-61680-2_67
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DOI: https://doi.org/10.1007/3-540-61680-2_67
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