A BSP/CGM algorithm for computing Euler tours in graphs

We describe a parallel algorithm using the BSP/CGM model (Bulk Synchronous Parallel/Coarse Grained Multicomputer) to obtain the Euler tours in graphs. It is based on the PRAM (parallel random access machine) algorithm by Caceres et al. For an input graph of n vertices and m edges, the algorithm requires local computation time of O((m+n)/p), O((m+n'p) memory and O(logp) communication rounds, where p is the number of processors. To our knowledge there are no other parallel algorithms under the coarse-grained models for the Euler tours in graphs. The proposed algorithm is implemented using MPI (message passing interface) and the C language. The parallel program runs on a Beowulf with 66 nodes. The implementation results confirm the theoretical complexity results of the algorithm.