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A universal hashing scheme is a randomized algorithm that selects a hash function h among a family of such functions, in such a way that the probability of a collision of any two distinct keys is 1/m, where m is the number of distinct hash values desired—independently of the two keys. Universal hashing ensures (in a probabilistic sense) that ...
A perfect hash function for the four names shown A minimal perfect hash function for the four names shown. In computer science, a perfect hash function h for a set S is a hash function that maps distinct elements in S to a set of m integers, with no collisions. In mathematical terms, it is an injective function.
A hash table uses a hash function to compute an index, also called a hash code, into an array of buckets or slots, from which the desired value can be found. During lookup, the key is hashed and the resulting hash indicates where the corresponding value is stored. A map implemented by a hash table is called a hash map.
In a typical document classification task, the input to the machine learning algorithm (both during learning and classification) is free text. From this, a bag of words (BOW) representation is constructed: the individual tokens are extracted and counted, and each distinct token in the training set defines a feature (independent variable) of each of the documents in both the training and test sets.
In contrast, in most traditional hash tables, a change in the number of array slots causes nearly all keys to be remapped because the mapping between the keys and the slots is defined by a modular operation. Consistent hashing evenly distributes cache keys across shards, even if some of the shards crash or become unavailable. [3]
In words, when given an x, it is not possible to find another x' such that the hashing function would create a collision. A hash function has strong collision resistance when, given a hashing function H, no arbitrary x and x' can be found where H(x)=H(x'). In words, no two x's can be found where the hashing function would create a collision.
A cryptographic hash function must be able to withstand all known types of cryptanalytic attack. In theoretical cryptography, the security level of a cryptographic hash function has been defined using the following properties: Pre-image resistance Given a hash value h, it should be difficult to find any message m such that h = hash(m).
This is exactly the probability of collision we would expect if the hash function assigned truly random hash codes to every key. Sometimes, the definition is relaxed by a constant factor, only requiring collision probability O ( 1 / m ) {\displaystyle O(1/m)} rather than ≤ 1 / m {\displaystyle \leq 1/m} .