Set Membership with a Few Bit Probes

We consider the bit-probe complexity of the set membership problem, where a set S of size at most n from a universe of size m is to be represented as a short bit vector in order to answer membership queries of the form "Is x in S?" by adaptively probing the bit vector at t places. Let s(m,n,t) be the minimum number of bits of storage needed for such a scheme. Several recent works investigate s(m,n,t) for various ranges of the parameter; we obtain improvements over some of the bounds shown by Buhrman, Miltersen, Radhakrishnan, and Srinivasan (2002) and Alon and Feige (2009).