Representation of Edmonds' Algorithm for Finding Optimum Graph Branching on Associative Parallel Processors

Authors:
A. Sh. Nepomniaschaya
Affiliations:
Institute of Computational Mathematics and Mathematical Geophysics, Siberian Division, Russian Academy of Sciences, pr. Akademika Lavrent'eva 6, Novosibirsk, 630090 Russia
Venue:
Programming and Computing Software
Year:
2001

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Abstract

In the paper, an efficient parallel implementation of Edmonds' algorithm is suggested for finding optimum graph branching on an abstract model of the SIMD type with vertical data processing (STAR machine). For this, associative parallel algorithms for finding critical circuit and its contraction, as well as for unfolding embedded critical circuits, are constructed for directed weighted graphs represented as a list of arcs and their weights. It is shown that the execution of Edmonds' algorithm on a STAR machine requires O(nlogn) time, where nis the number of graph vertexes. Basic advantages of the parallel implementation of Edmonds' algorithm compared to its implementation on sequential computers are discussed.