Modeling the Parallelization of the Edmonds-Karp Algorithm and Application

Abstract

Many optimization problems can be reduced to the maximum flow problem in a network. However, the maximum flow problem is equivalent to the problem of the minimum cut, as shown by Fulkerson and Ford (Fulkerson & Ford, 1956). There are several algorithms of the graph’s cut, such as the Ford-Fulkerson algorithm (Ford & Fulkerson, 1962), the Edmonds-Karp algorithm (Edmonds & Karp, 1972) or the Goldberg-Tarjan algorithm (Goldberg & Tarjan, 1988). In this paper, we study the parallel computation of the Edmonds-Karp algorithm which is an optimized version of the Ford-Fulkerson algorithm. Indeed, this algorithm, when executed on large graphs, can be extremely slow, with a complexity of the order of O|V|.|E|2 (where |V| designates the number of vertices and |E| designates the number of the edges of the graph). So why we are studying its implementation on inexpensive parallel platforms such as OpenMp and GP-GPU. Our work also highlights the limits for parallel computing on this algorithm.

Gap Analysis of Ford-Fulkerson Algorithm and Edmonds-Karp Algorithm as Machine Learning Approach for Augmentation Path in the Maximum Flow Problem

“…The study was about a Traffic Management System that aims to reduce traffic congestion in the streets. This algorithm was used to solve the max-flow problems in planning, artificial vision, operational research, and optimization of the network (Chaibou, Tessa, Sié, & Faso, 2019). It also provides a solution in a flow network to find the maximum amount of flow.…”

“…The flow in the capacity of the residual will be increased until all paths will be saturated. This algorithm will solve the max flow problem by starting the process from the value of zero as long as the paths of the flow will be increasing (Chaibou, Tessa, Sié, & Faso, 2019).…”

“…The Edmonds-Karp algorithm process will be terminated once the possible paths have the nonzero capability. In terms of large paths, it is very slow to run, but as of now, it has a version that optimizes this problem (Chaibou, Tessa, Sié, & Faso, 2019). This paper aims to analyze the gaps of the Ford-Fulkerson Algorithm and the Edmonds-Karp Algorithm in solving the maximum flow problem and provide a comparative analysis between the two algorithms.…”