Systems and methods for generating a dense graph
First Claim
1. A method for generating a dense graph, the method comprising:
- (a) receiving a graph;
(b) calculating a density of the graph;
(c) computing a threshold to apply to the graph, the threshold including the density of the graph;
(d) determining whether the graph includes a first set of at least one node;
(e) determining whether a second set of at least one node from the first set meets the threshold;
(f) removing the at least one node of the second set from the graph upon determining that the at least one node of the second set meets the threshold, wherein the removing is performing to generate an updated graph;
(g) determining whether a density of the updated graph is greater than a density of the graph;
(h) replacing the graph with the updated graph upon determining that the density of the updated graph is greater than the density of the graph calculated during execution of the method;
(i) controlling a number of iterations of the method by changing a multiple of the density of the graph, wherein the multiple is greater than one,wherein the method is executed by one or more processors.
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Abstract
Methods and systems for generating a dense graph are described. One of the methods includes receiving a graph and computing a threshold to apply to the graph. The method further includes determining whether the graph includes a first set of at least one node, determining whether a second set of at least one node from the first set meets the threshold, and removing the at least one node of the second set concurrently from the graph upon determining that the at least one node of the second set meets the threshold. The operation of removing is performed to generate an updated graph. The method includes determining whether a density of the updated graph is greater than a density of the graph and replacing the graph within the updated graph upon determining that the density of the updated graph is greater than the density of the density of the graph.
56 Citations
20 Claims
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1. A method for generating a dense graph, the method comprising:
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(a) receiving a graph; (b) calculating a density of the graph; (c) computing a threshold to apply to the graph, the threshold including the density of the graph; (d) determining whether the graph includes a first set of at least one node; (e) determining whether a second set of at least one node from the first set meets the threshold; (f) removing the at least one node of the second set from the graph upon determining that the at least one node of the second set meets the threshold, wherein the removing is performing to generate an updated graph; (g) determining whether a density of the updated graph is greater than a density of the graph; (h) replacing the graph with the updated graph upon determining that the density of the updated graph is greater than the density of the graph calculated during execution of the method; (i) controlling a number of iterations of the method by changing a multiple of the density of the graph, wherein the multiple is greater than one, wherein the method is executed by one or more processors. - View Dependent Claims (2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16)
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17. A system for determining a subgraph within a graph, the system comprising:
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a memory device configured to receive the graph; one or more processors configured to; (a) calculate a density of the graph; (b) compute a threshold to apply to the graph, the threshold including the density of the graph; (c) determine whether the graph includes a first set of at least one node; (d) determine whether a second set of at least one node from the first set meets the threshold; (e) remove the at least one node of the second set from the graph upon determining that the at least one node of the second set meets the threshold, wherein the removal is performed to generate an updated graph; (f) determine whether a density of the updated graph is greater than a density of the graph; (g) replace the graph within the updated graph upon determining that the density of the updated graph is greater than the density of the graph calculated in (b); and (h) control a number of iterations of the method by changing a multiple of the density of the graph, wherein the multiple is greater than one. - View Dependent Claims (18, 19)
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20. A non-transitory computer-readable medium having instructions for causing a computer to execute a method comprising:
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(a) receiving a graph; (b) calculating a density of the graph; (c) computing a threshold to apply to the graph, the threshold including the density of the graph; (d) determining whether the graph includes a first set of at least one node; (e) determining whether a second set of at least one node from the first set meets the threshold; (f) removing the at least one node of the second set from the graph upon determining that the at least one node of the second set meets the threshold, wherein said removing is performed to generate an updated graph; (g) determining whether a density of the updated graph is greater than a density of the graph; (h) replacing the graph within the updated graph upon determining that the density of the updated graph is greater than the density of the graph calculated during execution of the method; and (i) controlling a number of iterations of the method by changing a multiple of the density of the graph, wherein the multiple is greater than one.
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Specification