A data structure for representing a set of n items from a umverse of m items, which uses space n + o(n) and accommodates membership queries m constant time is described. Both the data structure and the query algorithm are easy to ~mplement.

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Storing a Sparse Table with 0(1) Worst Case Access Time

A plurality of disparate communication network systems communicate with each other through the use of different physical media protocols. Each of the systems has at least one input and one output. A message routing system couples a transmitter at any one system input to a receiver at any other system output using a message format that is structure independent of the location of the receiver in the system. Each receiver/transmitter device coupled to any one system input has a unique, fixed and unchangeable identification code regardless of the communication network system to which it is connected. To couple a message from any one receiver/transmitter device to a second receiver/transmitter device at an unknown location within the communication network system, a message format is transmitted from the sending location containing the fixed, unique identification code of the receiving station. A routing system having a plurality of intermediate routing devices receives the message format and couples it to the receiving station at the unknown location using only the fixed, unique identification codes of the transmitting and receiving stations and the addresses of the intermediate routing devices for determining routing.

Message routing system for shared communication media networks

An efficient digital search algorithm that is based on an internal array structure called a double array, which combines the fast access of a matrix form with the compactness of a list form, is presented. Each arc of a digital search tree, called a DS-tree, can be computed from the double array in 0(1) time; that is to say, the worst-case time complexity for retrieving a key becomes 0(k) for the length k of that key. The double array is modified to make the size compact while maintaining fast access, and algorithms for retrieval, insertion, and deletion are presented. If the size of the double array is n+cm, where n is the number of nodes of the DS-tree, m is the number of input symbols, and c is a constant particular to each double array, then it is theoretically proved that the worst-case times of deletion and insertion are proportional to cm and cm/sup 2/, respectively, and are independent of n. Experimental results of building the double array incrementally for various sets of keys show that c has an extremely small value, ranging from 0.17 to 1.13. >

An efficient digital search algorithm by using a double-array structure

Using a trace of address references, the author compares the efficiency of several different hashing functions such as cyclic redundancy checking polynomials, Fletcher checksum, folding of address octets using the exclusive-OR operation, and bit extraction from the address. Guidelines are provided for determining the size of hash masks required to achieve a specified level of performance. >

A comparison of hashing schemes for address lookup in computer networks

Perfect hashing

A method is presented for building minimal perfect hash functions, i.e., functions which allow single probe retrieval from minimally sized tables of identifier sets. A proof of existence for minimal perfect hash functions of a special type (reciprocal type) is given. Two algorithms for determining hash functions of reciprocal type are presented and their practical limitations are discussed. Further, some application results are given and compared with those of earlier approaches for perfect hashing.

G. Jaeschke

Papers

Reciprocal hashing: a method for generating minimal perfect hashing functions