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Finding a partition that simplifies graph analysis is a hard problem, but one that has applications to scientific computing, VLSI circuit design, and task scheduling in multiprocessor computers, among others. [1] Recently, the graph partition problem has gained importance due to its application for clustering and detection of cliques in social ...
Graph partition into subgraphs of specific types (triangles, isomorphic subgraphs, Hamiltonian subgraphs, forests, perfect matchings) are known NP-complete. Partition into cliques is the same problem as coloring the complement of the given graph. A related problem is to find a partition that is optimal terms of the number of edges between parts ...
1 Examples and types of graphs. 2 Graph coloring. ... This is a list of graph theory topics, ... Graph partition; Graph pebbling;
Generally, a partition is a division of a whole into non-overlapping parts. Among the kinds of partitions considered in mathematics are partition of a set or an ordered partition of a set,
The dotted line in red represents a cut with three crossing edges. The dashed line in green represents one of the minimum cuts of this graph, crossing only two edges. [1] In graph theory, a minimum cut or min-cut of a graph is a cut (a partition of the vertices of a graph into two disjoint subsets) that is minimal in some metric.
Gather/scatter is a type of memory addressing that at once collects (gathers) from, or stores (scatters) data to, multiple, arbitrary indices. Examples of its use include sparse linear algebra operations, [1] sorting algorithms, fast Fourier transforms, [2] and some computational graph theory problems. [3]
In graph theory, a part of mathematics, a k-partite graph is a graph whose vertices are (or can be) partitioned into k different independent sets. Equivalently, it is a graph that can be colored with k colors, so that no two endpoints of an edge have the same color. When k = 2 these are the bipartite graphs, and when k = 3 they are called the ...
In numerical analysis, nested dissection is a divide and conquer heuristic for the solution of sparse symmetric systems of linear equations based on graph partitioning. Nested dissection was introduced by George (1973); the name was suggested by Garrett Birkhoff. [1] Nested dissection consists of the following steps: