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

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Book cover SOFSEM 2013: Theory and Practice of Computer Science (SOFSEM 2013)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 7741))

Abstract

There 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.

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Author information

Authors and Affiliations

  1. Fakultät für Informatik und Automatisierung, Technische Universität Ilmenau, Germany

    Michael Rink

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  1. Michael Rink
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Editor information

Editors and Affiliations

  1. Department of Mathematics and Computer Science, University of Amsterdam, Plantage Muidergracht 24, 1018 TV, Amsterdam, The Netherlands

    Peter van Emde Boas

  2. Informatics Institute, Intelligent Systems Lab Amsterdam, University of Amsterdam, Science Park 904, 1098 XH, Amsterdam, The Netherlands

    Frans C. A. Groen

  3. Department of Civil Engineering and Computer Science, University of Rome Tor Vergata, Via del Politecnico 1, 00133, Rome, Italy

    Giuseppe F. Italiano

  4. Institute of Computing Science, Poznan University of Technology, ul. Piotrowo 2, 60-965, Poznan, Poland

    Jerzy Nawrocki

  5. Hasso-Plattner-Institute for Software Systems Engineering, Prof.-Dr.-Helmert-Str. 2-3, 14482, Potsdam, Germany

    Harald Sack

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Rink, M. (2013). Mixed Hypergraphs for Linear-Time Construction of Denser Hashing-Based Data Structures. In: van Emde Boas, P., Groen, F.C.A., Italiano, G.F., Nawrocki, J., Sack, H. (eds) SOFSEM 2013: Theory and Practice of Computer Science. SOFSEM 2013. Lecture Notes in Computer Science, vol 7741. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-35843-2_31

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  • DOI: https://doi.org/10.1007/978-3-642-35843-2_31

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-35842-5

  • Online ISBN: 978-3-642-35843-2

  • eBook Packages: Computer ScienceComputer Science (R0)

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