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.
Highlights
In this paper, we study the parallelization of the Edmonds-Karp algorithm
We study the parallel computation of the Edmonds-Karp algorithm which is an optimized version of the Ford-Fulkerson algorithm
The relation (6) shows that the acceleration of this algorithm for very high values of M is majored to 3 3.4 Implementation on GPGPU To port the Edmonds-Karp algorithm on GP-GPU (General-purpose Processing on Graphics Processing Units), we have as well as when it comes to the OpenMP, identify the parallelizable zoned: the calculation for the search for the minimum residual capacity and the update of edges capabilities
Summary
We study the parallelization of the Edmonds-Karp algorithm. A formal approach of this algorithm was proposed by Lammich P. and Sefidgar S. The process stops when all possible paths with nonzero capability are exhausted. This algorithm, as simple as it looks, is very slow when run on large graphs. Edmonds and Karp had already proposed an algorithm parallelization and optimization approach for shared memory systems. Other parallel versions of this algorithm have been developed (Karger & Stein, 1996; Vineet & Narayanan, 2008). We analyze the complexity of the parallelization of this algorithm, we propose a parallel solution approach that we codify and test
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