Layout of embedding locally twisted cube into the extended theta mesh topology

A graph embedding is an important aspect in establishing equivalence of interconnections in parallel and distributed machines. Finding the minimum layout serves as a cost criterion for evaluating a good embedding. The binary hypercube is one of the most widely used topology for interconnection networks due to its simple, deadlock-free routing and broadcasting properties. The locally twisted cube is an important variant of the hypercube with the same number of vertices and connections but exhibits enhanced properties than its counterpart. In this paper we consider the problem of embedding an n-dimensional locally twisted cube into the extended rooted theta mesh in such a way as to minimize its layout.