Journal ArticleDOI
The complexity of congestion-1 embedding in a hypercube
Young Man Kim,Ten-Hwang Lai +1 more
TLDR
It is shown that any graph G can be embedded with unit congestion in a hypercube of dimension n ≥ max{6⌈log|V(G)|⌉, deg( G )}, but it is NP-complete to determine whether G is congestion-1 embeddable in a given hypercube, even if the source graph is connected.About:
This article is published in Journal of Algorithms.The article was published on 1991-04-01. It has received 22 citations till now. The article focuses on the topics: Graph embedding & Line graph.read more
Citations
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Book ChapterDOI
Recent Advances in Graph Partitioning
TL;DR: In this article, the authors survey recent trends in practical algorithms for balanced graph partitioning, point to applications, and discuss future research directions, and present a survey of the most popular algorithms.
Posted Content
Recent Advances in Graph Partitioning
TL;DR: Recent trends in practical algorithms for balanced graph partitioning are surveyed, applications are pointed to and future research directions are discussed.
Journal ArticleDOI
The complexity of counting self-avoiding walks in subgraphs of two-dimensional grids and hypercubes
TL;DR: This paper offers a partial answer to the question of Welsh: it is #P-complete to compute the number of self-avoiding walks of a given length in a subgraph of a two-dimensional grid.
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Algorithms for Mapping Parallel Processes onto Grid and Torus Architectures
TL;DR: In this article, the authors propose a communication-efficient bijective mapping between the blocks and the PEs, which is based on the same greedy algorithm used in this paper.
References
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Journal ArticleDOI
Topological properties of hypercubes
Y. Saad,M.H. Schultz +1 more
TL;DR: The authors examine the hypercube from the graph-theory point of view and consider those features that make its connectivity so appealing and propose a theoretical characterization of the n-cube as a graph.
Journal ArticleDOI
The cosmic cube
TL;DR: Cosmic Cube as discussed by the authors is a hardware simulation of a future VLSI implementation that will consist of single-chip nodes, which offers high degrees of concurrency in applications and suggests that future machines with thousands of nodes are both feasible and attractive.
Journal ArticleDOI
On the Mapping Problem
TL;DR: This mapping problem is formulated in graph theoretic terms and shown to be equivalent, in its most general form, to the graph isomorphism problem.
Proceedings ArticleDOI
The iPSC/2 direct-connect communications technology
TL;DR: The Direct-Connect router enhances the performance of the iPSC/2 system by reducing the message passing latency, increasing the node-to-node channel bandwidth and allowing simultaneous bi-directional message traffic between any two nodes.
Related Papers (5)
Efficient parallel algorithms for testing k -connectivity and finding disjoint s-t paths in graphs
Samir Khuller,Baruch Schieber +1 more