Topic
Hypercube graph
About: Hypercube graph is a research topic. Over the lifetime, 914 publications have been published within this topic receiving 19761 citations.
Papers published on a yearly basis
1 / 2
Papers
TL;DR: Efficient algorithms are presented for partitioning a graph into connected components, biconnected components and simple paths and each iteration produces a new path between two vertices already on paths.
Abstract: Efficient algorithms are presented for partitioning a graph into connected components, biconnected components and simple paths. The algorithm for partitioning of a graph into simple paths of iterative and each iteration produces a new path between two vertices already on paths. (The start vertex can be specified dynamically.) If V is the number of vertices and E is the number of edges, each algorithm requires time and space proportional to max (V, E) when executed on a random access computer.
1,146 citations
IBM1
TL;DR: The results are two fold: it is shown that graphs generated using the proposed random graph models exhibit the statistics observed on the Web graph, and additionally, that natural graph models proposed earlier do not exhibit them.
Abstract: The Web may be viewed as a directed graph each of whose vertices is a static HTML Web page, and each of whose edges corresponds to a hyperlink from one Web page to another. We propose and analyze random graph models inspired by a series of empirical observations on the Web. Our graph models differ from the traditional G/sub n,p/ models in two ways: 1. Independently chosen edges do not result in the statistics (degree distributions, clique multitudes) observed on the Web. Thus, edges in our model are statistically dependent on each other. 2. Our model introduces new vertices in the graph as time evolves. This captures the fact that the Web is changing with time. Our results are two fold: we show that graphs generated using our model exhibit the statistics observed on the Web graph, and additionally, that natural graph models proposed earlier do not exhibit them. This remains true even when these earlier models are generalized to account for the arrival of vertices over time. In particular, the sparse random graphs in our models exhibit properties that do not arise in far denser random graphs generated by Erdos-Renyi models.
822 citations
1 Oct 1947
TL;DR: A cubical graph is a simplicial 1-complex in which each 0-simplex is incident with just three 1-simples as discussed by the authors, and cubical graphs are simplicial simplicial 2-complexes.
Abstract: We begin with some definitions.A cubical graph is a simplicial 1-complex in which each 0-simplex is incident with just three 1-simplexes.
536 citations
17 Nov 1996
TL;DR: A key innovative feature of this parallel formulation is that it utilizes graph coloring to effectively parallelize both the coarsening and the refinement during the uncoarsening phase, making it possible to perform dynamic graph partition in adaptive computations without compromising quality.
Abstract: In this paper we present a parallel formulation of a multilevel k-way graph partitioning algorithm. The multilevel k-way partitioning algorithm reduces the size of the graph by collapsing vertices and edges (coarsening phase), finds a k-way partition of the smaller graph, and then it constructs a k-way partition for the original graph by projecting and refining the partition to successively finer graphs (uncoarsening phase). A key innovative feature of our parallel formulation is that it utilizes graph coloring to effectively parallelize both the coarsening and the refinement during the uncoarsening phase. Our algorithm is able to achieve a high degree of concurrency, while maintaining the high quality partitions produced by the serial algorithm. We test our scheme on a large number of graphs from finite element methods, and transportation domains. Our parallel formulation on Cray T3D, produces high quality 128-way partitions on 128 processors in a little over two seconds, for graphs with a million vertices. Thus our parallel algorithm makes it possible to perform dynamic graph partition in adaptive computations without compromising quality.
493 citations
TL;DR: A survey of existing methods of communication in usual networks, particularly the complete network, the ring, the torus, the grid, the hypercube, the cube connected cycles, the undirected de Bruijn graph, the stargraph, the shuffle-exchange graph, and the butterfly graph.
440 citations
Related Topics (5)
Performance Metrics
| Year | Papers |
|---|---|
| 2025 | 2 |
| 2024 | 1 |
| 2023 | 3 |
| 2022 | 6 |
| 2021 | 5 |
| 2020 | 4 |