Mapping pyramids into 3-D meshes

Abstract

Embedding one parallel architecture into another is very important in the area of parallel processing because parallel architectures can vary widely. Given a pyramid architecture of (4/sup N/-1)/3 nodes and height N, this paper presents a mapping method to embed the pyramid architecture into a 2/sup N-1-k//spl times/2/sup N-1-k//spl times/(4/sup k+1/+2)/3 mesh for 0/spl les/k/spl les/N-1. Our method has dilation max{4/sup k/, 2/sup N-2-k/} and expansion 1+2/(4k+1). When setting k=(N-2)/3, the pyramid can be embedded into a 2/sup (2N-1//3)/spl times/2/sup (2N-1//3)/spl times/[4/sup (N+1//3)+2]/3 mesh, and it has dilation and expansion 1+2/[4/sup (N+1//3)]. This result has can optimal expansion when N is sufficiently large and is superior to the previous mapping methods in terms of the same gauges.