Load Balancing 2-Phased Geometrically Based Problems

A k-weighted graph is a directed graph where each vertex has k associated weights. Partitioning such a graph so that each weight is roughly evenly divided into each piece is useful for balancing a parallel task with k distinct components. Such a goal arises in crash simulation, in which there there are 2 components. We present a 2-weighted graph partitioning algorithm, based on the Ham Sandwich Theorem, for graphs embedded in 2-space. We demonstrate that this algorithm runs in linear expected time and yields a good partition in practice. 1 Introduction When one endeavors to make a serious study of parallel algorithms, the problem of load balancing inevitably presents itself. Load balancing can be described as the process of dividing a problem or subproblem into a number of smaller problems equal to the number of processors at hand such that the running time of this problem or subproblem when executed in parallel on these processors is minimized. A problem can seldom be load balanced ..