Efficient Sequential and Parallel Algorithms for the Negative Cycle Problem

Dimitris J. Kavvadias, Grammati E. Pantziou, Paul G. Spirakis, Christos D. Zaroliagis

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).