Complexity of finding embeddings in a k-tree
SIAM Journal on Algebraic and Discrete Methods
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 trees in a hypercube is NP-complete
SIAM Journal on Computing
Concrete mathematics: a foundation for computer science
Concrete mathematics: a foundation for computer science
Deterministic sorting in nearly logarithmic time on the hypercube and related computers
STOC '90 Proceedings of the twenty-second annual ACM symposium on Theory of computing
Embedding mesh of trees in the hypercube
Journal of Parallel and Distributed Computing
Introduction to parallel algorithms and architectures: array, trees, hypercubes
Introduction to parallel algorithms and architectures: array, trees, hypercubes
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
On the complexity of the embedding problem for hypercube related graphs
Discrete Applied Mathematics
Pipelined parallel prefix computations, and sorting on a pipelined hypercube
Journal of Parallel and Distributed Computing
Embedding K-ary complete trees 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 Algorithms with Optimal Speedup for Bounded Treewidth
SIAM Journal on Computing
Parallel permutation and sorting algorithms and a new generalized connection network
Journal of the ACM (JACM)
ACM Transactions on Programming Languages and Systems (TOPLAS)
Efficient Dynamic Embedding of Arbitrary Binary Trees into Hypercubes
IRREGULAR '96 Proceedings of the Third International Workshop on Parallel Algorithms for Irregularly Structured Problems
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
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In this paper, we present a one-to-one embedding of a graph with bounded treewidth into its optimal hypercube. This is the first time that embeddings of graphs with a highly irregular structure into hypercubes are investigated. The presented embedding achieves dilation of at most 3 [log((d + 1)(t + 1))] + 8 and node-congestion of at most O(d(dt)3), where t denotes the treewidth of the graph and d denotes the maximal degree of a vertex in the graph. Provided that the graph is given by its tree-decomposition the embedding can be computed efficiently on the hypercube itself. In particular, the embedding of a graph with constant treewidth and constant degree can be computed in time O(log2(n)log log log(n)log*(n)). For graphs with constant treewidth, a minimal tree-decomposition can be computed efficiently in parallel due to a result of Bodlaender and Hagerup. In this case, the embedding can be computed on the hypercube in time O(log2(n)(d2 + log(n) log log2(n))).