Stencils and problem partitionings: their influence on the performance of multiple processor systems
IEEE Transactions on Computers
Algorithmics: theory & practice
Algorithmics: theory & practice
Partitioning Problems in Parallel, Pipeline, and Distributed Computing
IEEE Transactions on Computers
Performance Analysis of k-ary n-cube Interconnection Networks
IEEE Transactions on Computers
Partitioning sparse matrices with eigenvectors of graphs
SIAM Journal on Matrix Analysis and Applications
A distributed memory LAPSE: parallel simulation of message-passing programs
PADS '94 Proceedings of the eighth workshop on Parallel and distributed simulation
Processor allocation policies for message-passing parallel computers
SIGMETRICS '94 Proceedings of the 1994 ACM SIGMETRICS conference on Measurement and modeling of computer systems
Rectilinear partitioning of irregular data parallel computations
Journal of Parallel and Distributed Computing
Communication algorithms in k-ary n-cube interconnection networks
Information Processing Letters
Analytical modelling of networks in multicomputer systems under bursty and batch arrival traffic
The Journal of Supercomputing
Mutually independent Hamiltonian cycles in k-ary n-cubes when k is odd
AMERICAN-MATH'10 Proceedings of the 2010 American conference on Applied mathematics
Matching preclusion for k-ary n-cubes
Discrete Applied Mathematics
Hamiltonian cycles passing through linear forests in k-ary n-cubes
Discrete Applied Mathematics
Determining the conditional diagnosability of k-ary n-cubes under the MM* model
SIROCCO'11 Proceedings of the 18th international conference on Structural information and communication complexity
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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, 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 theoretical results are then applied to compute a lower bounding function in branch-and-bound partitioning algorithms and to establish the optimality of some irregular partitions.