On k-ary n-cubes: theory and applications

Weizhen Mao, David M. Nicol
2003 Discrete Applied Mathematics  
7 Many parallel processing applications have communication patterns that can be viewed as graphs called k-ary n-cubes, whose special cases include rings, hypercubes and tori. In this paper, 9 combinatorial properties of k-ary n-cubes are examined. In particular, the problem of characterizing the subgraph of a given number of nodes with the maximum edge count is studied. These 11 theoretical results are then applied to compute a lower bounding function in branch-and-bound partitioning algorithms
more » ... and to establish the optimality of some irregular partitions. ? 2002 Pub-13 lished by Elsevier Science B.V.
doi:10.1016/s0166-218x(02)00238-x fatcat:aeqcxwdkmfh6na2lh2ir7t4q4q