Revisiting explicit adaptive two-probe schemes

Abstract In the bitprobe model the primary concern is the number of bits that must be probed in a data structure in order to answer queries, and how constraining the number probes affects the storage requirements. In this note we revisit an explicit membership scheme of Radhakrishnan, Raman, and Rao [ESA 2001], which stores an n = 2 element subset of a universe [ 1 , m ] , occupies O ( m 2 / 3 ) bits, and supports membership queries in t = 2 bit probes. We show that, with a small modification to their storage scheme, their query scheme also works for n = 3 elements.