Almost random graphs with simple hash functions

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 + ) 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 wellknown technique of random offsets. While keeping the space needed to store the description of h1 and h2 at O(n ), for < 1 fixed arbitrarily, we obtain a much smaller (constant) evaluation time than previous constructions of this kind, which involved Siegel's high-performance hash classes. The main new technique is the combined analysis of the graph structure and the inner structure of the hash functions, as well as a new way of looking at the cycle structure of random (multi)graphs. The construction may be applied to improve on ...

• Type: Conference
• Year: 2003
• Where: STOC
• Authors: Martin Dietzfelbinger, Philipp Woelfel
• Keywords: Algorithms, D-wise Independent Hashing, Keywords Random Graphs, STOC 2003, Uniform Hashing Permission