Binary Dissection: Variants & Applications

Partitioning is an important issue in a variety of applications. Two examples are domain decomposition for parallel computing and color image quantization. In the former we need to partition a computational task over many processors; in the latter we need to partition a high resolution color space into a small number of representative colors. In both cases, partitioning most be done in a manner that fields good results as defined by an application-specific metric. Binary dissection is a technique that has been widely used to partition non-uniform domains over parallel computers. It proceeds by recursively partitioning the given domain into two parts, such that each part has approximately equal computational load. The basic dissection algorithm does not consider the perimeter, surface area or aspect ratio of the two sub-regions generated at each step and can thus yield decompositions that have poor communication to computation ratios. We have developed and implemented several variants of the binary dissection approach that attempt to remedy this limitation. are faster than the basic algorithm, can be applied to a variety of problems, and are amenable to parallelization. We first present the Parametric Binary Dissection (PBD) algorithm, which takes into account volume and surface area when partitioning computational domains for use in parallel computing applications. We then consider another variant, the Fast Adaptive Dissection (FAD) algorithm which provides rapid spatial partitioning for use in color image quantization. We describe the performance of PBD and FAD on representative problems and present ways of parallelizing the PBD algorithm on or 3-d meshes and on hypercubes.