Embedding meshes into locally twisted cubes

Abstract

As a newly introduced interconnection network for parallel computing, the locally twisted cube possesses many desirable properties. In this paper, mesh embeddings in locally twisted cubes are studied. Let LTQ n ( V, E) denote the n-dimensional locally twisted cube. We present three major results in this paper: (1) For any integer n ⩾ 1, a 2 × 2 n−1 mesh can be embedded in LTQ n with dilation 1 and expansion 1. (2) For any integer n ⩾ 4, two node-disjoint 4 × 2 n−3 meshes can be embedded in LTQ n with dilation 1 and expansion 2. (3) For any integer n ⩾ 3, a 4 × (2 n−2 − 1) mesh can be embedded in LTQ n with dilation 2. The first two results are optimal in the sense that the dilations of all embeddings are 1. The embedding of the 2 × 2 n−1 mesh is also optimal in terms of expansion. We also present the analysis of 2 p × 2 q mesh embedding in locally twisted cubes.