Biased Predecessor Search

TL;DR

This paper develops new data structures for predecessor search in a bounded universe that adapt to query distribution, achieving entropy-dependent query times with various space complexities.

Contribution

It introduces data structures that achieve entropy-based query times with bounded space and handles unknown distributions and weighted elements.

Findings

Expected query times logarithmic in query distribution entropy

Linear space data structures with sublinear entropy-based query times

Effective handling of unknown query distributions and weighted elements

Abstract

We consider the problem of performing predecessor searches in a bounded universe while achieving query times that depend on the distribution of queries. We obtain several data structures with various properties: in particular, we give data structures that achieve expected query times logarithmic in the entropy of the distribution of queries but with space bounded in terms of universe size, as well as data structures that use only linear space but with query times that are higher (but still sublinear) functions of the entropy. For these structures, the distribution is assumed to be known. We also consider individual query times on universe elements with general weights, as well as the case when the distribution is not known in advance.