Hashing is a fundamental technique in Computer Science, and perfect hashing, which guarantees constant-time lookup, has particular theoretical and practical importance. The algorithm of Fredman, Koml'os, and Szemer'edi [8], augmented by Dietzfelbinger, et al. [7], is a simple perfect hashing scheme that has not seen extensive use due to poor practical performance. In this paper, we develop modifications to the previous techniques that result in a fast, space-efficient algorithm. We show the resulting algorithm is comparable to hash algorithms used in several popular dictionary libraries but is more flexible and has better theoretical performance. 1

In Hash Tables for the Standard Template Library, Barreiro, Fraley, and Musser propose a restructuring and extension of the STL requirements for associative containers to accommodate hash table implementations. This paper gives the rationale for the proposed changes. i CONTENTS ii Contents 1 Introduction 1 2 How hash tables work 2 2.1 Table organizations : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : 2 2.2 Uniform hashing assumption : : : : : : : : : : : : : : : : : : : : : : : : : : 2 2.3 Intermittent or gradual resizing : : : : : : : : : : : : : : : : : : : : : : : : : 3 3 Advantages and disadvantages of hash tables 3 4 Differences in associative container interfaces 5 5 Using hash tables: a sample program 9 5.1 A program using a set : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : 9 5.2 The same program, using a hash set : : : : : : : : : : : : : : : : : : : : : : 10 6 Remaining issues 1 INTRODUCTION 1 1 Introduction The requirements for the C++...