Pseudo-random graphs and bit probe schemes with one-sided error

We study probabilistic bit-probe schemes for the membership problem. Given a set A of at most n elements from the universe of size m we organize such a structure that queries of type “x ∈ A?” can be answered very quickly. H. Buhrman, P.B. Miltersen, J. Radhakrishnan, and S. Venkatesh proposed a bit-probe scheme based on expanders. Their scheme needs space of O(n log m) bits. The scheme has a randomized algorithm processing queries; it needs to read only one randomly chosen bit from the memory to answer a query. For every x the answer is correct with high probability (with two-sided errors). In this paper we show that for the same problem there exists a bitprobe scheme with one-sided error that needs space of O(n log2 m + poly(log m)) bits. The difference with the model of Buhrman, Miltersen, Radhakrishnan, and Venkatesh is that we consider a bit-probe scheme with an auxiliary word. This means that in our scheme the memory is split into two parts of different size: the main sto...

• Type: Journal
• Year: 2011
• Where: CORR
• Authors: Andrei E. Romashchenko
• Keywords: Combinatorial Object, CORR 2011, Education, Pseudo Random Generator, Randomized Algorithm