Pyramidal systems for computer vision
Simulating binary trees on hypercubes
VLSI Algorithms and Architectures
Embedding of d-dimensional grids into optimal hypercubes
SPAA '89 Proceedings of the first annual ACM symposium on Parallel algorithms and architectures
Embedding mesh of trees in the hypercube
Journal of Parallel and Distributed Computing
Embedding of grids into optimal hypercubes
SIAM Journal on Computing
Efficient embeddings of trees in hypercubes
SIAM Journal on Computing
Dynamic tree embeddings in butterflies and hypercubes
SIAM Journal on Computing
Taking random walks to grow trees in hypercubes
Journal of the ACM (JACM)
Embedding K-ary complete trees into hypercubes
Journal of Parallel and Distributed Computing
Dilation-5 embedding of 3-dimensional grids into hypercubes
Journal of Parallel and Distributed Computing
Embedding ladders and caterpillars into the hypercube
Discrete Applied Mathematics - Special issue: network communications broadcasting and gossiping
Parallel permutation and sorting algorithms and a new generalized connection network
Journal of the ACM (JACM)
ACM Transactions on Programming Languages and Systems (TOPLAS)
Embedding Graphs with Bounded Treewidth into Optimal Hypercubes
STACS '96 Proceedings of the 13th Annual Symposium on Theoretical Aspects of Computer Science
A General Method for Efficient Embeddings of Graphs into Optimal Hypercubes
Euro-Par '96 Proceedings of the Second International Euro-Par Conference on Parallel Processing - Volume I
On distributed computation rate optimization for deploying cloud computing programming frameworks
ACM SIGMETRICS Performance Evaluation Review
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In this paper, a deterministic algorithm for dynamically embedding binary trees into hypercubes is presented. Because of a known lower bound, any such algorithm must use either randomization or migration, i.e., remapping of tree vertices, to obtain an embedding of trees into hypercubes with small dilation, load, and expansion simultaneously. Using migration of previously mapped tree vertices, the presented algorithm constructs a dynamic embedding which achieves dilation of at most 9, unit load, nearly optimal expansion, and constant edge- and node-congestion. This is the first dynamic embedding that achieves these bounds simultaneously. Moreover, the embedding can be computed efficiently on the hypercube itself. The amortized time for each spawning step is bounded by O(log2(L)), if in each step at most L new leaves are spawned. From this construction, a dynamic embedding of large binary trees into hypercubes is derived which achieves dilation of at most 6 and nearly optimal load. Similarly, this embedding can be constructed with nearly optimal load ρ on the hypercube itself in amortized time O(ρ . log2(L/ρ)) per spawning step, if in each step at most L new leaves are added.