Finding a negative cycle in a directed graph

Abstract

We present an algorithm implemented on a pointer machine 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 linear Space O(n+e). The best previous result was due to D.Maier [5]. His algorithm is running on a random access machine in worst case Time O(n(e+nlog n/log nlog n)) and uses Space O(e+nlog n/log nlog n).