A mathematical game and its applications to the design of interconnection networks

In this paper we propose a mathematical game, called the ball-arrangement game (BAG). A game with a different set of rules (e.g., permissible moves) gives rise to a different network, and the algorithm that solves the game gives rise to a routing algorithm in that network. Based on the insights provided by BAG, we propose several new classes of symmetric and modular networks, called super Cayley graphs, that have optimal (intercluster) diameters and average (intercluster) distances, small (intercluster) node degrees, high bisection bandwidth, strong embedding capability, and optimal communication algorithms given their (intercluster) node degrees.