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	.:: General Purpose Hash Function Algorithms - By Arash Partow ::.
		When algorithms which contain hash functions are analyzed it is generally assumed that hash functions have a complexity of O(1), that is why look-ups for data in a hash-table are said to be of O(1) complexity, where as look-ups of data in maps (Red-Black Trees) are said to be of O(logn) complexity.
		This is achieved through the use of multiple distinct hash functions and also by allowing the result of a query for the existance of a particular type to have a certain amount of error.
		It is a simple hash function using a strange set of possible seeds which all constitute a pattern of 31....31...31 etc, it seems to be very similar to the DJB hash function.
	www.partow.net /programming/hashfunctions (1811 words)

	Hash function - Wikipedia, the free encyclopedia
		A hash function or hash algorithm is a function for summarizing or probabilistically identifying data.
		Hash functions that are truly random with uniform output (including most cryptographic hash functions) yield good performance because, on average, only one or two probes will be needed (depending on the load factor).
		universal hashing by stinson from university of nabraska lincoln
	en.wikipedia.org /wiki/Hash_function (1194 words)

	Hash function
		A hash function is a function that converts an input from a (typically) large domain into an output in a (typically) smaller range (the hash value, often a subset of the integers).
		Formally speaking, a hash function is defined by its domain (typically variable-length strings of bytes), by its range (typically fixed length bit-sequences) and by the defining function (call this function H).
		Hash tables, a major application for hash functions, speed up the lookup of a record of information, given a key (note: this use of the word key is separate from its meaning as a code for encrypting data).
	www.brainyencyclopedia.com /encyclopedia/h/ha/hash_function.html (940 words)

	Perfect hash function - Wikipedia, the free encyclopedia
		Perfect hash functions are hash functions which guarantee to map different keys to different numbers.
		Using a perfect hash function is best at situations where there is a large dataset which is not updated frequently, and many look-ups into it.
		F is a minimal perfect hash function iff F(j)=F(k) implies j=k and there exists an integer a such that the range of F is a..
	en.wikipedia.org /wiki/Perfect_hash_function (220 words)

	Perfect hash function -- Facts, Info, and Encyclopedia article (Site not responding. Last check: 2007-11-05)
		Perfect hash functions are (additional info and facts about hash function) hash functions which guarantee (The 15th letter of the Roman alphabet) O(1) operations (The quality of being intricate and compounded) complexity when used in a (additional info and facts about hash table) hash table.
		This is opposed to a general hash function, which may, in some conditions, require a number of look-ups that is proportional to the table's size - O(n) operations, due to (additional info and facts about hash collision) hash collisions.
		F is a minimal perfect hash function (additional info and facts about iff) iff F(j)=F(k) implies j=k and there exists an integer a such that the range of F is a..
	www.absoluteastronomy.com /encyclopedia/p/pe/perfect_hash_function.htm (374 words)

	Perfect hash function (Site not responding. Last check: 2007-11-05)
		Perfect hash functions are hash functions which guarantee O(1) operations complexity when used in a hash table; In other words, a hash table that uses a perfect hash function guarantees that retrieving any value will take no more than some constant time, regardless of the table's size.
		This is opposed to a general hash function, which may, in some conditions, require a number of look-ups that is proportional to the table's size - O(n) operations.
		A specific perfect hash function may achieve this operation complexity constraint by guaranteeing that for a certain list of keys (see hash table), no two keys get the same hash value.
	www.sciencedaily.com /encyclopedia/perfect_hash_function (276 words)

	CIS 22: Hash Table Data Structure
		Hash Table is a data structure in which keys are mapped to array positions by a hash function.
		Hash Function is a function which, when applied to the key, produces an integer which can be used as an address in a hash table.
		Perfect Hash Function is a function which, when applied to all the members of the set of items to be stored in a hash table, produces a unique set of integers within some suitable range.
	acc6.its.brooklyn.cuny.edu /~cis22/hashing/Hash_Table_Hash_Function.html (543 words)

	Robert's Midterm Project = Hashing (Site not responding. Last check: 2007-11-05)
		Rarely did the hashing functions succeed in generating keys that didn't need to be modded by the table size or involve going over the table size and then subtracting the table size to bring it back in range.
		Another simple way to generate a perfect hashing function on a subset is to make a subset that works for a given hashing function.
		It's much easier and memory efficient to generate a perfect subset for a given hash function than it is to generate a perfect hash function for a given subset.
	gridley.res.carleton.edu /~hirair/cs227 (490 words)

	Perfect Hashing
		Initial hash returns (A,B), final hash is A^tab[B] The perfect hash algorithm I use isn't a Pearson hash.
		If perfect hashing is implemented as a special table for Pearson's hash (the usual implementation), minimal perfect hashing is not always possible, with probabilities given in the table below.
		For example, the hash which stores a sorted table of all keywords, and the location of each keyword is its hash, is a minimal perfect hash of n keywords into 0..n-1.
	www.burtleburtle.net /bob/hash/perfect.html (2077 words)

	The Hash Table Library
		Hash tables, sometimes also known as associative arrays, or scatter tables, are a data structure that offers fast lookup, insertion, and deletion of (key, value) pairs.
		Hashing was discovered and first published and implemented on computers in the early 1950s, and is based on a simple idea: transform the key to a number (the hash process), and then use that number to index a table.
		Return the maximum size of the hash table; this is the value used in the final modulo operation in the hash function.
	www.math.utah.edu /~beebe/software/hash/hash.html (2765 words)

	The Hash ADT (Site not responding. Last check: 2007-11-05)
		A hash table is a data structure that holds key-value pairs.
		Hashing is the technique that maps an object to a position in the array based on the object’s key using the hash function.
		The thing to remember is that the Hash ADT consists of a bucket array and a hash function that maps an object’s key to an index in the array.
	www.cis.cau.edu /123/notes/HashTableADT.htm (837 words)

	CS 200 Lecture 10, Page 1
		Hashing involves a hash table (an array that holds key values and pointers to the rest of the record) and a hash function that is used to decide where in the hash table the particular key/pointer goes.
		The hash function is a function that takes key values as input and produces integers that are legal positions in the hash table array.
		Thus, if the hash table array were an array of length N, a legal hash function for this hash table should always produce an integer which is greater than or equal to 0 and less than N. Ideally, the hash function should produce a different integer for any key.
	www.users.csbsju.edu /~lziegler/cs200/200-10a.html (571 words)

	Almost Perfect Hashing: (Site not responding. Last check: 2007-11-05)
		Hashing: Hashing is a method of ordering data members by a hash value in a hash table using a hash function that determines the hash value by performing some operations on the data with expected O(n) asymptotic performance.
		Hash Key: A value that can be used to identify a data member or group of data members that are in a hash table.
		Hash Value: The value that is computed by sending the key of data that is to be inserted or searched for to the hash function.
	userpages.umbc.edu /~cespos2/441project.html (1564 words)

	Paul Brown's Weblog
		My first comment is on perfect hash functions and probably lies off the beaten path for people who didn't have a hard-core CS education.
		A perfect hash function is pre-constructed based on a known (at compile time) set of keys and has the property that the function returns a distinct values for distinct keys.
		function is a good idea in the context of a reasonable (i.e., known and finite) number of strings.
	radio.weblogs.com /0119894/categories/java/2003/06/18.html (391 words)

	[No title]
		That means, given a set of n keys, this determines a hash function that maps each of those keys into a value in 0..n-1 with no collisions.
		The perfect hash function first uses a normal hash function on the key to determine (a,b) such that the pair (a,b) is distinct for all keys, then it computes a^scramble[tab[b]] to get the final perfect hash.
		The key is hashed to a pair (a,b) where a in 0..alen-1 and b in 0..blen-1.
	burtleburtle.net /bob/c/perfect.c (1327 words)

	TOPIC #12 HASHING BY CHAINING
		Perfect hashing functions can be found only under certain conditons.
		A hash value selects one of these buckets, which is then searched sequentially until the target object is located or an empty slot is encountered.
		If the keys are uniformly distributed over the table, then hashing takes expected time O(n) under a computational model in which the computation of a hash function is done in O(1) worst-case time.
	www.cs.mcgill.ca /~cs251/OldCourses/1997/topic12 (968 words)

	Perfect Hashing
		If perfect hashing is implemented as a special table for Pearson's hash (the usual implementation), minimal perfect hashing is not always possible, with probabilities given in the table below.
		For example, the hash which stores a sorted table of all keywords, and the location of each keyword is its hash, is a minimal perfect hash of n keywords into 0..n-1.
		This sorted-table minimal perfect hash might not even be slower than Pearson perfect hashing, since the sorted-table hash must do a comparison per bit of key, while the Pearson hash must do an operation for every character of the key.
	burtleburtle.net /bob/hash/perfect.html (2077 words)

	ONJava.com -- Optimizing Hash Functions For a Perfect Map
		A hash function cannot generally guarantee every data item maps to a different index, so the structure of a hash table is complicated by needing to maintain a list at every index, allowing multiple objects to be held at any index.
		implementations with perfect hash functions are much simpler than using generic hash functions; they consist of two arrays, one for the keys and one to hold all corresponding values.
		A hash function which maps each key to a unique index and leaves no empty entries in the table is called a minimal perfect hash function).
	www.onjava.com /pub/a/onjava/2001/01/25/hash_functions.html (946 words)

	Perfect Hash (Site not responding. Last check: 2007-11-05)
		Perfect Software, Inc. has obtained a government contract to examine text flowing through a high-speed network for the occurrence of certain words.
		A perfect hash function maps its input directly to a fully occupied table.
		Your job is to construct the perfect hash functions from the lists of words in each table.
	acm.uva.es /p/v1/188.html (349 words)

	[No title] (Site not responding. Last check: 2007-11-05)
		HASHING Section 7.4 hash function division - h(key)= key % table_size multiplicative method choose c between 0 and 1.
		Under double hashing, the rehash paths for two keys that rehash to the same slot will diverge.
		Rehashing: 1) rh(i,j) = (i+j)%tablesize - uses number of times function is applied 2) Use a random permutation of numbers between 1 and t t=tablesize p1, p2,..., pt --- random permutations rh(i,j) = (h(key)+pj)%tablesize no two rehashss of same key conflict so the 2nd rehashs would use p2.
	www.unf.edu /public/cop3530/ree/Notes/sec7.4 (448 words)

	gperf(1) - generate a perfect hash function from a key set
		Generate the static table of keywords as a static global variable, rather than hiding it inside of the lookup function (which is the default behavior).
		Select the key positions used in the hash function.
		Also, the meta-character ’’ causes the generated hash* function to consider ALL key positions, and $ indicates the ‘‘final character’’ of a key, e.g., $,1,2,4,6-10.
	www.gsp.com /cgi-bin/man.cgi?section=1&topic=gperf (622 words)

	Perfect Minimal Hash Generator (Site not responding. Last check: 2007-11-05)
		generates perfect minimal hash functions for a set of keys using the algorithm described in "Optimal algorithms for minimal perfect hashing", G. Havas, B.S. Majewski.
		The first line of each pair is a string containing a key, and the second line is an integer which is the desired hash code.
		Choose a number N larger than K. This is the number of vertices in a graph G, and also the size of the resulting table.
	www.amk.ca /python/code/perfect-hash.html (293 words)

	Chapter 8
		The hash function takes some value that you give it and converts it to an address that is in your array.
		The hash function has some requirements that stipulate whether or not the hash function is a good has function or not.
		This is where you apply a second hash to the value to find a new location for the result.
	www.cs.uregina.ca /~peckham/cs210b/notes/Chapter_8.html (1230 words)

	Options
		Duplicate hash values occur for two reasons: * Since `gperf' does not backtrack it is possible for it to process all your input keywords without finding a unique mapping for each word.
		Furthermore, the meta-character '' causes the generated hash* function to consider all character positions in each key, whereas '$' instructs the hash function to use the "final character" of a key (this is the only way to use a character position greater than 126, incidentally).
		A set of examples for generating perfect hash tables and functions for Ada, C, and G++, Pascal, and Modula 2 and 3 reserved words are distributed with this release.
	docs.freebsd.org /info/gperf/gperf.info.Options.html (1547 words)

	Project 4 - Hash Tables
		To compute the hash function for any integer is going to require a number of data structures.
		Once this minimal perfect hash table is constructed, you are ready to begin reading the text file and counting key words.
		To examine a token, simply pass it through the hash function discussed in Section 2.3 and see if the word is currently in the hash table.
	www.cs.wisc.edu /~mattmcc/cs367/projects/p4.html (2446 words)

	PHF - Perfect Hash Function (Site not responding. Last check: 2007-11-05)
		PHF is a acronym that can contains many meanings which are listed below.
		There may be many popular meanings for PHF with the most popular definition being that of Perfect Hash Function
		If you have more information or know of another definition for PHF, please let us know so that we can review it and add that information to our database.
	www.auditmypc.com /acronym/PHF.asp (167 words)

	[No title] (Site not responding. Last check: 2007-11-05)
		The general idea for the perfect hash function generator was inspired by Keith Bostic's algorithm written in C, and distributed to net.sources around 1984.
		A helpful heuristic is that the larger the hash value range, the easier it is for `gperf' to find and generate a perfect hash function.
		Their default function prototypes are as follows: static int hash (char str, int len); int in_word_set (char str, int len); By default, the generated `hash' function returns an integer value created by adding LEN to several user-specified STR key positions indexed into an "associated values" table stored in a local static array.
	www.math.psu.edu /local_doc/info/gperf.info (6284 words)

	A New Practical Algorithm for the Construction of a Perfect Hash Function - Atici, Stinson, Wei (ResearchIndex)
		Abstract: A perfect hash function for a subset X of f0; 1; \Delta \Delta \Delta ; n \Gamma 1g is an injection h from X into the set f0; 1; \Delta \Delta \Delta ; m \Gamma 1g.
		Perfect hash functions are useful for the compact storage and fast retrieval of frequently used objects.
		In this paper, we discuss some new practical algorithms for efficient construction of perfect hash functions, and we analyze their complexity and program size.
	citeseer.ist.psu.edu /5319.html (490 words)

	Perfect Hash Function Generator
		generates a hash function that considers positions 1,2,4,6,7,8,9,10, plus the last character in each key (which may differ for each key, obviously).
		Using this option usually means that the generated hash function is no longer perfect.
		Negative values are useful for limiting the overall size of the generated hash table, though this usually increases the number of duplicate hash values.
	www.delorie.com /gnu/docs/gperf/gperf_18.html (912 words)

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