Optimal layouts of midimew networks

Midimew networks are mesh-connected networks derived from a subset of degree-4 circulant graphs. They have minimum diameter and average distance among all degree-4 circulant graphs, and are better than some of the most common topologies for parallel computers in terms of various cost measures. Among the many midimew networks, the rectangular ones appear to be most suitable for practical implementation. Unfortunately, with the normal way of laying out these networks on a 2D plane, long cross wires that grow with the size of the network exist. In this paper, we propose ways to lay out rectangular midimew networks in a 2D grid so that the length of the longest wire is at most a small constant. We prove that these constants are optimal under the assumption that rows and columns are moved as a whole during the layout process.