Abstract :
This paper considers the communication patterns arising from the partition of geometrical domain into sub-domains, when data is exchanged between processors assigned to adjacent sub-domains. It presents the algorithm constructing bipartite graphs covering the graph representation of the partitioned domain, as well as the scheduling algorithm utilizing the coloring of the bipartite graphs. Specifically, when the communication pattern arises from the partition of a 2D geometric area, the planar graph representation of the domain is partitioned into not more than two bipartite graphs and a third graph with maximum vertex valency 2, by means of the presented algorithm. In the general case, the algorithm finds h — 1 or fewer bipartite graphs, where h is the maximum number of neighbors. Finally, the task of message scheduling is reduced to a set of independent scheduling problems over the bipartite graphs. The algorithms are supported by a theoretical discussion on their correctness and efficiency.
