Almost random graphs with simple hash functions

  • Authors:
  • Martin Dietzfelbinger;Philipp Woelfel

  • Affiliations:
  • Technische Universität Ilmenau, Germany, Ilmenau, Germany;Universität Dortmund, Germany

  • Venue:
  • Proceedings of the thirty-fifth annual ACM symposium on Theory of computing
  • Year:
  • 2003

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Abstract

We describe a simple randomized construction for generating pairs of hash functions h1,h2 from a universe U to ranges V = [m] = (0,1,...,m-1) and W = [m] so that for every key set S ⊆ U with n = |S| ≤ m/(1 + ε) the (random) bipartite (multi)graph with node set V ∪ W and edge set (h1(x),h2(x))| x ∈ S exhibits a structure that is essentially random. The construction combines d-wise independent classes for d a relatively small constant with the well-known technique of random offsets. While keeping the space needed to store the description of h1 and h2 at O(nζ), for ζ