Practicable layouts for optimal circulant graphs

Circulant graphs have been deeply studied in technical literature. Midimew networks are a class of distance-related optimal circulant graphs of degree four which have applications in network engineering and coding theory. In this research, a new layout for Midimew networks which keeps the maximum link length under the value √5 is presented, considering unitary length as the subjacent mesh link´s length. The most interesting Midimew sizes are studied: dense and quasidense cases, with bounded link length layouts in both cases, although the proposed algorithm is also valid for other network sizes. These results improve a previously known result in a maximum factor of √5. Also, the number of planar layers necessary to implement this layout is studied. In addition, an expandability method is presented which enables network expansion without modifying existing nodes or links, except those needed to connect to new nodes. Finally, this layout is compared to the classical folded Torus. When considering both physical and topological distances and propagation delays our proposal is clearly competitive against Tori.