Optimal Turn Prohibition for Deadlock Prevention in Networks With Regular Topologies

In this paper, we consider the problem of constructing minimal cycle-breaking connectivity preserving sets of turns for graphs that model communication networks, as a method to prevent deadlocks. Cycle-breaking provides for deadlock-free wormhole routing constrained by turns prohibited at some nodes. We present lower and upper bounds for minimal cardinalities of cycle-breaking connectivity preserving sets for several classes of graphs such as homogeneous meshes, \mbi p-ary \mbi n-cubes, cube-connected cycles, hexagonal and honeycomb meshes, tori, etc.