Given a directed graph where edges are associated with weights which are not necessarily positive, we are concerned with the problem of finding all the elementary cycles with negative total weights. Algorithms to find all the elementary cycles, or to detect, if one exists, a negative cycle in such a graph are well explored. However, finding all the elementary cycles with negative cost appears to be unexplored. We develop an algorithm to do this based on the "divide-and-conquer" paradigm, and evaluate its performance on some numerical experiments.
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