Data and process mapping of sparse graph systems in a distributed environment (non-reviewed)

Methods employed for extracting parallel grains from a given sparse graph are varied and heuristic in nature, since it is NP-Hard to find the maximally balanced connected partition for a general graph [1]. In many cases, e.g. the GR -"Greedy Algorithm" [2], PI - "Principal Inertia" algorithms [3], RGB - "Recursive Graph Bisection" [4], 1DTF - The "ID Topology Frontal"; algorithm [5] and RSB - "Recursive Spectral Bisection" [6,7], systems are decomposed based upon the number of available processors without regard to the graph topology, which leads to inefficient data structuring (i.e. redundant storage, high communication costs and indiscriminate load balancing). An efficient methodology for regrouping and mapping a given decomposition is developed in this work. It is based on the "elimination-tree," or e-tree, data structure of [8]. The e-tree is a spanning tree for the given graph, and is utilized as a data structure to guide parallel processing. The mapping function assigns a "label," gamma, to each vertex: V rarr {1,2,...,n}. "Label classes" are defined as an ordered set, or list, of labels and contain vertices which can be processed in parallel after the vertices of all previously defined classes have been processed. A symbolic factorization technique is used to create these label classes, or sub-graphs, from G(A).