An efficient algorithm for embedding exchanged hypercubes into grids

Graph embedding is an important technology in simulating parallel structures and designing VLSI layout. Hypercube is one of the most significant interconnection networks in parallel computing systems. The exchanged hypercube is an important variant of the hypercube, which is obtained by systematically deleting edges from a hypercube. It not only retains several valuable and desirable properties of the hypercube, but also has lower hardware cost. In this paper, we first give an exact formula of minimum wirelength of exchanged hypercube layout into a grid. Furthermore, we propose an O(N) algorithm for embedding exchanged hypercube into a gird with load 1, expansion 1 and minimum wirelength and derive a linear layout of exchanged hypercube with minimum number of tracks and efficient layout areas. Finally, we present simulation experiments of our embedding algorithm on network overhead and total wirelength, which conduce to estimate the total wirelength and chip area.