Mixed Hypergraphs for Linear-Time Construction of Denser Hashing-Based Data Structures

Abstract

AbstractThere are several hashing-based data structures whose space utilization (keys per table cells) directly depends on the edge density threshold for the appearance of a 2-core in some underlying random k-uniform hypergraph. We show that by modifying these data structures such that the k-uniform hypergraphs are replaced by certain non-uniform hypergraphs their space utilization can be improved. These non-uniform hypergraphs are a mixture of uniform hypergraphs each with a linear number of edges but with different edge sizes. In the case of two different edge sizes we give a solution for the optimal (expected) number of edges of each size such that the 2-core threshold for the resulting mixed hypergraph is maximized. For suitable edge sizes we obtain optimal thresholds for mixed hypergraphs up to 0.920, improving the maximum 2-core threshold for any random k-uniform hypergraph, which is about 0.818.KeywordsSpace UsageGlobal Minimum PointRaptor CodeEdge SizeRateless CodeThese keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.