On k - ary n - cubes : Theory and Applications 1

Many parallel processing networks can be viewed as graphs called k-ary n-cubes, whose special cases include rings, hypercubes and toruses. In this paper, combinatorial properties of k-ary n-cubes are explored. In particular, the problem of characterizing the subgraph of a given number of nodes with the maximum edge count is studied. These theoretical results are then used to compute a lower bounding function in branch-andbound partitioning algorithms and to establish the optimality of some irregular partitions. An extended abstract of this paper (without any proofs and missing some theorems) has been submitted to the 1995 International Parallel Processing Symposium, with the permission of its Program Chair to simultaneously submit this full paper to an archival journal. This work was supported in part by NSF grant CCR-9210372. This work was supported in part by NASA under NAS1-19480 while the author was on sabbatical at the Institute for Computer Applications in Science and Engineering, NASA Langley Research Center, Hampton, VA 23681. It was also supported in part by NSF grant CCR-9201195.