Local graph partitioning using evolving sets
First Claim
1. A system for targeted partitioning of a graph, comprising:
- memory for storing instructions for partitioning the graph; and
at least one processor to execute the instructions to determine conductance of a subset of the graph;
a sequencing component, stored in the memory and executable by the at least one processor, to evolve a current set of vertices by expanding or contracting the current set based on a number of edges of one or more boundary vertices, the one or more boundary vertices comprising a subset of the vertices of the current set that are within a minimum distance to a boundary of the current set; and
an analysis component, stored in the memory and executable by the at least one processor, to determine a conductance of the current set and terminate the evolution when the conductance of the current set is equal to or less than a threshold.
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Accused Products
Abstract
Providing for local graph partitioning using an evolving set process is disclosed herein. By way of example, a computer processor can be configured to execute local partitioning based on evolving set instructions. The instructions can be employed to transition a set of analyzed vertices of a graph until a segment of the graph with small conductance is identified. A transitioning algorithm can expand or contract the analyzed set of vertices based on characteristics of vertices at a boundary of the analyzed set. Accordingly, as the set of analyzed vertices becomes large, significant processing efficiency is gained by employing the characteristics of boundary vertices to transition the set or determine conductance, rather than all vertices of the analyzed set.
9 Citations
20 Claims
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1. A system for targeted partitioning of a graph, comprising:
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memory for storing instructions for partitioning the graph; and at least one processor to execute the instructions to determine conductance of a subset of the graph; a sequencing component, stored in the memory and executable by the at least one processor, to evolve a current set of vertices by expanding or contracting the current set based on a number of edges of one or more boundary vertices, the one or more boundary vertices comprising a subset of the vertices of the current set that are within a minimum distance to a boundary of the current set; and an analysis component, stored in the memory and executable by the at least one processor, to determine a conductance of the current set and terminate the evolution when the conductance of the current set is equal to or less than a threshold. - View Dependent Claims (2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14)
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15. A computer-executable method for targeted partitioning of a graph, comprising:
employing at least one processor for executing local partitioning instructions to identify a subset of the graph pertinent to a starting set, the instructions comprising; transforming a current set of vertices of the graph to a subsequent set as a function of edge calculations of boundary vertices of the current set, the boundary vertices comprising a subset of the vertices of the current set at a boundary of the current set; and verifying that vertices of the current set comprise a pertinent subset of the graph if conductance of the boundary vertices meets a threshold conductance; and outputting vertices of the pertinent subset from the at least one processor. - View Dependent Claims (16, 17, 18, 19)
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20. A graph partitioning system for targeted partitioning of a graph comprising vertices and edges, the system comprising:
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memory for storing instructions for partitioning the graph; and at least one processor to execute the instructions to determine conductance of a subset of the graph; a sequencing component, stored in the memory and executable by the at least one processor, to evolve a current set of vertices by expanding or contracting the current set based on a number of edges of one or more boundary vertices, the boundary vertices comprising a subset of the vertices of the current set at a boundary of the current set; an analysis component, stored in the memory and executable by the at least one processor, to determine a conductance of the current set and terminate the evolution if the conductance of the current set is equal to or less than a threshold; a termination component, stored in the memory and executable by the at least one processor, to stop execution of the instructions if time t is equal to a maximum run time T, or upon the conductance of the current set dropping below the threshold; and a reporting component, stored in the memory and executable by the at least one processor, to output the vertices of the current set.
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Specification