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In mathematics, a graph partition is the reduction of a graph to a smaller graph by partitioning its set of nodes into mutually exclusive groups. Edges of the original graph that cross between the groups will produce edges in the partitioned graph. If the number of resulting edges is small compared to the original graph, then the partitioned graph may be better suited for analysis and problem-solving than the original. 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. Recently, the graph partition problem has gained importance due to its application for clustering and detection of cliques in social, pathological and biological networks. For a survey on recent trends in computational methods and applications see . Two common examples of graph partitioning are minimum cut and maximum cut problems. Typically, graph partition problems fall under the category of NP-hard problems. Solutions to these problems are generally derived using heuristics and approximation algorithms. However, uniform graph partitioning or a balanced graph partition problem can be shown to be NP-complete to approximate within any finite factor. Even for special graph classes such as trees and grids, no reasonable approximation algorithms exist, unless P=NP. Grids are a particularly interesting case since they model the graphs resulting from Finite Element Model (FEM) simulations. When not only the number of edges between the components is approximated, but also the sizes of the components, it can be shown that no reasonable fully polynomial algorithms exist for these graphs. Consider a graph G = (V, E), where V denotes the set of n vertices and E the set of edges. For a (k,v) balanced partition problem, the objective is to partition G into k components of at most size v · (n/k), while minimizing the capacity of the edges between separate components.

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Related publications (1)

Spinner: Scalable Graph Partitioning in the Cloud

Andreas Loukas, Dionysios Logothetis

In this paper, we present a graph partitioning algorithm to partition graphs with trillions of edges. To achieve such scale, our solution leverages the vertex-centric Pregel abstraction provided by Giraph, a system for large-scale graph analytics. We designed our algorithm to compute partitions with high locality and fair balance, and focused on the characteristics necessary to reach wide adoption by practitioners in production. Our solution can (i) scale to massive graphs and thousands of compute cores, (ii) efficiently adapt partitions to changes to graphs and compute environments, and (iii) seamlessly integrate in existing systems without additional infrastructure. We evaluate our solution on the Facebook and Instagram graphs, as well as on other large-scale, real-world graphs. We show that it is scalable and computes partitionings with quality comparable, and sometimes outperforming, existing solutions. By integrating the computed partitionings in Giraph, we speedup various real-world applications by up to a factor of 5.6 compared to default hash-partitioning.

Ieee2017

Related concepts (2)

Related courses (1)

CS-455: Topics in theoretical computer science

The students gain an in-depth knowledge of several current and emerging areas of theoretical computer science. The course familiarizes them with advanced techniques, and develops an understanding of f

Graph partition

Graph (discrete mathematics)

In discrete mathematics, and more specifically in graph theory, a graph is a structure amounting to a set of objects in which some pairs of the objects are in some sense "related". The objects correspond to mathematical abstractions called vertices (also called nodes or points) and each of the related pairs of vertices is called an edge (also called link or line). Typically, a graph is depicted in diagrammatic form as a set of dots or circles for the vertices, joined by lines or curves for the edges.