Deterministic splitter finding in a stream with constant storage and guarantees

Abstract

In this paper the well-known problem of finding the median of an ordered set is studied under a very restrictive streaming model with sequential read-only access to the data. Only a constant number of reference objects from the stream can be stored for comparison with subsequent stream elements. A first non-trivial bound of distance to the extrema of the set is presented for a single pass over streams which do not reveal their total size n. For cases with known size, an algorithm is given which guarantees a distance of Ω(n 1-ε) to the extrema, which is an ε-approximation for the proven best bound possible. © 2006 Springer-Verlag Berlin/Heidelberg.