Abstract. We present here an algorithm for detecting (and outputting, if exists) a negative cycle in an n-vertex planar digraph G with real edge weights. Its running time ranges from O(n) up to O(n 1.5 log n) as a certain topological measure of G varies from 1 up to Θ(n). Moreover, an efficient CREW PRAM implementation is given. Our algorithm applies also to digraphs whose genus γ is o(n).
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