Negative Cost Girth Problem using Map-Reduce Framework

On a graph with a negative cost cycle, the shortest path is undefined, but the number of edges of the shortest negative cost cycle could be computed. It is called Neg-ative Cost Girth (NCG). The NCG problem is applied in many optimization issues such as scheduling and model verification. The existing polynomial algorithms suffer from high computation and memory consumption. In this paper, a powerful Map-Reduce framework imple-mented to find the NCG of a graph. The proposed algo-rithm runs in O(log k) parallel time over O(n3) on each Hadoop nodes, where n, k are the size of the graph and the value of NCG, respectively. The Hadoop implemen-tation of the algorithm shows that the total execution time is reduced by 50% compared with polynomial algo-rithms, especially in large networks concerning increas-ing the numbers of Hadoop nodes. The result proves the efficiency of the approach for solving the NCG problem to process big data in a parallel and distributed way.