Abstract
AbstractR-MAT (for Recursive MATrix) is a simple, widely used model for generating graphs with a power law degree distribution, a small diameter, and communitys structure. It is particularly attractive for generating very large graphs because edges can be generated independently by an arbitrary number of processors. However, current R-MAT generators need time logarithmic in the number of nodes for generating an edge— constant time for generating one bit at a time for node IDs of the connected nodes. We achieve constant time per edge by precomputing pieces of node IDs of logarithmic length. Using an alias table data structure, these pieces can then be sampled in constant time. This simple technique leads to practical improvements by an order of magnitude. This further pushes the limits of attainable graph size and makes generation overhead negligible in most situations.
Highlights
Graphs are the universal abstraction of relations between objects
Developing algorithms that process large graphs is often limited by the size of the available graphs
R-MAT is simple, models power law degree distributions, and produces graphs with a community structure that is somewhat similar to complex real-world networks
Summary
Graphs are the universal abstraction of relations between objects. With the “big data” revolution, many applications have emerged that have to process huge graphs (e.g., social networks, web graphs, “brain graphs”, gene sequencing data). R-MAT is simple, models power law degree distributions, and produces graphs with a community structure that is somewhat similar to complex real-world networks. Our technique can be adapted to a other applications that define random objects recursively The edge is placed in the upper left quadrant with probability a, in the upper right with probability b, in the lower left with probability c, and in the lower right quadrant with probability d The process repeats this subdivision k times until a single entry of the adjacency matrix is determined; see Figure 1. If x − x < w, element e is returned, otherwise the alias e is returned.
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