Mapping pyramids into 3-D meshes

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^N-1)/3 nodes and height N, this paper presents a mapping method to embed the pyramid architecture into a 2^N-1-k×2^N-1-k×(4 ^k+1+2)/3 mesh for 0⩽k⩽N-1. Our method has dilation max{4^k, 2^N-2-k} and expansion 1+2/(4k+1). When setting k=(N-2)/3, the pyramid can be embedded into a 2^(2N-1//3)×2sup (2N-1//3)×[4^(N+1//3)+2]3 mesh, and it has dilation and expansion 1+2/[4^(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