Abstract

. A static data structure problem consists of a set of data D, a set of queries Q and a function f with domain D \ThetaQ. Given a space bound b, a (good) solution to the problem is an encoding e : D ! f0; 1g b , so that for any y, f(x; y) can be determined (quickly) by probing e(x). The worst case number of probes needed is C b (f ), the bit probe complexity of f . We study the properties of the complexity measure C b (\Delta). 1 Introduction and preliminaries Elias and Flower [5] introduced the following model of retrieval problems: A set D, called the set of data, a set Q, called the set of queries and a set A, called the set of answers is given, along with a function f : D \Theta Q ! A. The problem is to devise a scheme for encoding elements of D into data structures in the memory of a random access machine. When an x 2 D has been encoded, it should be possible at a later point in time to come forward with any y 2 Q and efficiently compute f(x; y) using random access to...

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