Finding succinct ordered minimal perfect hashing functions

An ordered minimal perfect hash table is one in which no collisions occur among a predefined set of keys, no space is unused, and the data are placed in the table in order. A new method for creating ordered minimal perfect hashing functions is presented. The method presented is based on a method developed by Fox, Heath, Daoud, and Chen, but it creates hash functions with representation space requirements closer to the theoretical lower bound. The method presented requires approximately 10% less space to represent generated hash functions, and is easier to implement than Fox et al's. However, a higher time complexity makes it practical for small sets only (< 1000)

Fast Flow Analysis with Godel Hashes

Abstract—Flow analysis, such as control-flow, data-flow, and exception-flow analysis, usually depends on relational operations on flow sets. Unfortunately, set related operations, such as inclusion and equality, are usually very expensive. They can easily take more than 97 % of the total analyzing time, even in a very simple analysis. We attack this performance bottleneck by proposing Gödel hashes to enable fast and precise flow analysis. Gödel hashes is an ultra compact, partial-order-preserving, fast and perfect hashing mechanism, inspired by the proofs of Gödel’s incompleteness theorems. Compared with array-, tree-, traditional hash-, and bit vector-backed set implementations, we find Gödel hashes to be tens or even hundreds of times faster for performance in the critical operations of inclusion and equality. We apply Gödel hashes in real-world analysis for object-oriented programs. The instrumented analysis is tens of times faster than the one with original data structures on DaCapo benchmarks. I

Internal hashing for dynamic and static tables

This tutorial discusses one of the oldest problems in computing: how to search and retrieve keyed information from a list in the least amount of time. Hashing - a technique that mathematically converts a key into a storage address - is one of the best methods of finding and retrieving information associated with a unique identifying key. We briefly survey techniques which have evolved over the past 25 years and then introduce more recent research results for extremely compact and fast methods based on per­fect and minimal perfect hashing. Perfect and minimal perfect hashing is useful for rapid lookup in a static table such as keywords in a compiler, spelling checkers, and database management systems. The results presented here show techniques for constructing long lists which can be searched in one memo­ry reference.KEYWORDS AND PHRASES: Key-to-address transformation, hash coding, hash table, scatter table, bucket hashing, perfect hashing, minimal perfect hashin

Comparison of Perfect Hashing Methods

This study was conducted to compare two minimal perfect hashing method Chang's method and Jaeschke's method. Since hashing is a widely used technique for store data in symbol table and the data are strings of characters, this study f use on the performance of these methods with the letter-oriented set and gives their run time performance curves. Through the analysis of run time and space complexity, an optimal method is given to make each algorithm performance well

A letter oriented minimal perfect rehashing scheme based upon reciprocal hashing

至今為止，處理掙態文字資料的赫序函數大多只能應用於存取少量的文字資料。本文 中，我們辱提出一種適於處理較多文字資料的最佳完美赫序函數之設計法；我們的靈 感來自Chang(1986b) 之倒數式的文字赫序法。應用我們的方法，不但能處理數百個以 上的文字資料，且透過簡單快速的赫序函數之運算，即可達到資料存取的目的。 參考文獻 1.Chang,C.C.,(1984a):The Styd of an Ordered Minimal Perfect Hashing Scheme, Communications of the Association for Computing Machinery, Vol. 27, No. 4, April 1984, pp. 384-387. 2.Chang,C.C.,(1984b):An Ordered Minimal Perfect Hashing Scheme Base upon E uler's Theorem, Information Sciences, Vol. 32, No. 3, June 1984, pp. 165- 172. 3.Chang,C.C.(1986a):A Scheme for Constructing Ordered Minimal Pefect Hashi ng Function, to appear in Information Sciences, 1986. 4.Chang,C.C.(1986b) :Letter-Oriented Reciprocal Hashing Scheme, to appear in the Information Sciences, 1986. 5.Chang,C.C.and Lee, R.C.,(1986):A Letter Oriented Minimal Perfect Hashing Scheme, to appear in the Computer Journal, 1986