Searching in constant time and minimum space
Andrej Brodnik · 1996
This report deals with techniques for minimal space representation of a subset of elements from a bounded universe so that various types of searches can be performed in constant time. In particular, we introduce a data structure to represent a subset of N elements of [0�:::�M;1] in a number of bits close to the information-theoretic minimum and use the structure to answer membership queries in constant time. Next, we describe a representation of an arbitrary subset of points on an M M grid such that closest neighbour queries (under L1 and L1) can be performed in constant time. This structure requires M 2 + o(M 2) bits. Finally, under a byte overlap model of memory we present an M + o(M) bit, constant time solution to the dynamic one-dimensional closest neighbour problem (hence, also union-split-find and priority queue problems) on [0�:::�M; 1].