Parallel algorithm for finding an Eulerian path in an undirected graph

Authors:
Akio Tada;Daisaburo Yoshioka;Eiichi Mukai;Yoshimi Matsumoto
Affiliations:
Sojo University, Faculty of Computer and Information Sciences, Kumamoto City, Japan;Sojo University, Faculty of Computer and Information Sciences, Kumamoto City, Japan;Sojo University, Faculty of Computer and Information Science, Kumamoto City, Japan;Sojo University, Faculty of Computer and Information Science, Kumamoto City, Japan
Venue:
MATH'08 Proceedings of the 13th WSEAS international conference on Applied mathematics
Year:
2008

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Abstract

There is Fleury's algorithm as a sequential algorithm for finding an Eulerian path in an undirected graph. However, we cannot find a parallel algorithm for this problem. In this paper, we proposed an efficient parallel algorithm for finding an Eulerian path in an undirected graph with n vertices and m edges on a CREW-PRAM model. Namely, the proposed algorithm initially determines whether or not a given graph has an Eulerian path. Next, we divide each vertex into several new vertices which have a maximum of 2 edge degrees, and connect between new vertices by edges. Consequently, we find one Eulerian path in the given graph. The proposed algorithm requires O(n + m) processors and O(log(n + m)) time on a CREW-PRAM model.