Universal hashing implementation

In hashing there is a hash function that maps keys to some values.

Hashing Data Structure

But these hashing function may lead to collision that is two or more keys are mapped to same value. Chain hashing avoids collision.

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The idea is to make each cell of hash table point to a linked list of records that have same hash function value. To insert a node into the hash table, we need to find the hash index for the given key.

And it could be calculated using the hash function. Insert : Move to the bucket corresponds to the above calculated hash index and insert the new node at the end of the list. Delete : To delete a node from hash table, calculate the hash index for the key, move to the bucket corresponds to the calculated hash index, search the list in the current bucket to find and remove the node with the given key if found.

Please refer Hashing Set 2 Separate Chaining for details. Attention reader! Get hold of all the important Java Foundation and Collections concepts with the Fundamentals of Java and Java Collections Course at a student-friendly price and become industry ready.

Writing code in comment? Please use ide. Skip to content. Related Articles. Recommended Articles. Area of the largest square that can be formed from the given length sticks using Hashing. Article Contributed By :. Current difficulty : Medium. Easy Normal Medium Hard Expert. Improved By :. Most popular in Hash. Most visited in Java. Load Comments. We use cookies to ensure you have the best browsing experience on our website.In mathematics and computinguniversal hashing in a randomized algorithm or data structure refers to selecting a hash function at random from a family of hash functions with a certain mathematical property see definition below.

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This guarantees a low number of collisions in expectationeven if the data is chosen by an adversary. Many universal families are known for hashing integers, vectors, stringsand their evaluation is often very efficient.

Universal hashing has numerous uses in computer science, for example in implementations of hash tablesrandomized algorithmsand cryptography. This means that all data keys land in the same bin, making hashing useless. Furthermore, a deterministic hash function does not allow for rehashing : sometimes the input data turns out to be bad for the hash function e.

The solution to these problems is to pick a function randomly from a family of hash functions. This is exactly the probability of collision we would expect if the hash function assigned truly random hash codes to every key. This concept was introduced by Carter and Wegman [1] inand has found numerous applications in computer science see, for example [2]. Many, but not all, universal families have the following stronger uniform difference property :. The uniform difference property is stronger.

Pairwise independence is sometimes called strong universality. Another property is uniformity. Universality does not imply uniformity. However, strong universality does imply uniformity.

Since a shift by a constant is sometimes irrelevant in applications e. For some applications such as hash tablesit is important for the least significant bits of the hash values to be also universal. Unfortunately, the same is not true of merely universal families.

Several hash table implementations are based on universal hashing. In such applications, typically the software chooses a new hash function only after it notices that "too many" keys have collided; until then, the same hash function continues to be used over and over.

Some collision resolution schemes, such as dynamic perfect hashingpick a new hash function every time there is a collision. Other collision resolution schemes, such as cuckoo hashing and 2-choice hashingallow a number of collisions before picking a new hash function.

A survey of fastest known universal and strongly universal hash functions for integers, vectors, and strings is found in.

However, the adversary has to make this choice before or independent of the algorithm's random choice of a hash function. If the adversary can observe the random choice of the algorithm, randomness serves no purpose, and the situation is the same as deterministic hashing. The second and third guarantee are typically used in conjunction with rehashing. Universality guarantees that the number of repetitions is a geometric random variable. Since any computer data can be represented as one or more machine words, one generally needs hash functions for three types of domains: machine words "integers" ; fixed-length vectors of machine words; and variable-length vectors "strings".

This section refers to the case of hashing integers that fit in machines words; thus, operations like multiplication, addition, division, etc. This is a single iteration of a linear congruential generator. Thus the collision probability is.

The state of the art for hashing integers is the multiply-shift scheme described by Dietzfelbinger et al. In mathematical notation, this is.

18-3 Universal Hashing

To obtain a truly 'universal' hash function, one can use the multiply-add-shift scheme. This section is concerned with hashing a fixed-length vector of machine words. In practice, if double-precision arithmetic is available, this is instantiated with the multiply-shift hash family of hash functions.

It is possible to halve the number of multiplications, which roughly translates to a two-fold speed-up in practice.

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The following hash family is universal: [14]. Thus, the algorithm runs at a "rate" of one multiplication per word of input. The same scheme can also be used for hashing integers, by interpreting their bits as vectors of bytes.A hash function is any function that can be used to map data of arbitrary size to fixed-size values.

The values returned by a hash function are called hash valueshash codesdigestsor simply hashes. The values are usually used to index a fixed-size table called a hash table. Use of a hash function to index a hash table is called hashing or scatter storage addressing. Hash functions and their associated hash tables are used in data storage and retrieval applications to access data in a small and nearly constant time per retrieval, and require an amount of storage space only fractionally greater than the total space required for the data or records themselves.

Hashing is a computationally and storage space efficient form of data access which avoids the non-linear access time of ordered and unordered lists and structured trees, and the often exponential storage requirements of direct access of state spaces of large or variable-length keys. Use of hash functions relies on statistical properties of key and function interaction: worst case behavior is intolerably bad with a vanishingly small probability, and average case behavior can be nearly optimal minimal collisions.

Hash functions are related to and often confused with checksumscheck digitsfingerprintslossy compressionrandomization functionserror-correcting codesand ciphers. Although the concepts overlap to some extent, each one has its own uses and requirements and is designed and optimized differently. The hash functions differ from the concepts numbered mainly in terms of data integrity. A hash function takes an input as a key, which is associated with a datum or record and used to identify it to the data storage and retrieval application.

The keys may be fixed length, like an integer, or variable length, like a name. In some cases, the key is the datum itself. The output is a hash code used to index a hash table holding the data or records, or pointers to them. A good hash function satisfies two basic properties: 1 it should be very fast to compute; 2 it should minimize duplication of output values collisions. Hash functions rely on generating favorable probability distributions for their effectiveness, reducing access time to nearly constant.

High table loading factors, pathological key sets and poorly designed hash functions can result in access times approaching linear in the number of items in the table. Hash functions can be designed to give best worst-case performance, [Notes 1] good performance under high table loading factors, and in special cases, perfect collisionless mapping of keys into hash codes.

A necessary adjunct to the hash function is a collision-resolution method that employs an auxiliary data structure like linked listsor systematic probing of the table to find an empty slot. Hash functions are used in conjunction with Hash table to store and retrieve data items or data records.

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The hash function translates the key associated with each datum or record into a hash code which is used to index the hash table. When an item is to be added to the table, the hash code may index an empty slot also called a bucketin which case the item is added to the table there.

If the hash code indexes a full slot, some kind of collision resolution is required: the new item may be omitted not added to the tableor replace the old item, or it can be added to the table in some other location by a specified procedure.

That procedure depends on the structure of the hash table: In chained hashingeach slot is the head of a linked list or chain, and items that collide at the slot are added to the chain. Chains may be kept in random order and searched linearly, or in serial order, or as a self-ordering list by frequency to speed up access.

In open address hashingthe table is probed starting from the occupied slot in a specified manner, usually by linear probingquadratic probingor double hashing until an open slot is located or the entire table is probed overflow. Searching for the item follows the same procedure until the item is located, an open slot is found or the entire table has been searched item not in table.

universal hashing implementation

Hash functions are also used to build caches for large data sets stored in slow media. A cache is generally simpler than a hashed search table, since any collision can be resolved by discarding or writing back the older of the two colliding items.This time, we'll delve into the details required to implement document similarity.

We'll first define feature extraction and how it is tightly coupled with MinHashing, then we'll talk about hash functions including djb2a and more generally, universal hash functions. Finally, we'll show how we can compute MinHash signatures, which estimate Jaccard Similarity, and we'll show how we can further sample these signatures using Locality Sensitive Hashing so that we can quickly and efficiently find clusters of similar documents.

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Feature construction is an endless field of study. For this example fixed length character shingles are used. Shingling is the process of choosing subsets of strings in a document such that the shingles encode word content and word ordering. In practice, depending on document size, k, the shingle size, is tuned to ensure that created shingles are as unique as possible.

If chosen well, comparing two sets of shingles to deduce document similarity will have low levels of false positives when sets of shingles from candidate matching documents are compared. Choosing the size of the shingles for the documents being analyzed is a crucial parameter. This means shingles will be created for every two characters.

For a suitably large document, if shingles were compared, the algorithm would find that there would likely be significant overlap leading to the conclusion that two documents are identical -- when in fact, the shingle parameter wasn't tuned properly, leading to false positives. In English, the average word is 5 letters long. For short documents, choosing 5 or 6 characters as shingle size is a viable choice, while longer documents would benefit from double the word length.

Optimal shingle size will vary based on language and word length. While English word length was used as an example, other alphabets and tokens can just as easily be used with equal success. We compare the set of shingles generated from two different sentences: 1 "The quick brown fox jumps over the lazy dog" and 2 "abcdefghijklmnopqrstuvwxyz ".

In the scala session below, we show that the set of shingles generated indicate that the two documents are exactly equal, which is a false positive. The shingle size parameter should be chosen carefully depending on the application.

Given a properly chosen shingle size, the shingling of the document will encode both the ordering and the content of the underlying text. Given the shingles of two documents, with properly chosen parameters, we could compute their set intersection to determine the similarity measure between the documents.

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However, as the document size grows, so does the number of shingles required to represent the document. If we can sample the shingles to still accurately reflect the contents of the document, we can compress the size of the signature required to determine document similarity.

universal hashing implementation

In fact, MinHash, as we will discuss later, samples the hash functions for each shingle, always choosing the lowest value, while LSH samples the MinHash signatures to further compress the document signature.

We discuss each of these in detail in later sections. In order to convert the shingles to an integer value which can be further hashed by our universal hash functionsa suitable hash function must chosen that is both quick and has a low collision rate. In order to MinHash, we'll need to first convert a shingle string to an integer hashes value, which can be further passed to the universal hash functions. In our case, we used the djb2a hash function, known for few collisions and super fast computation.

Another readily available hash function is MurMurHash. It is capable of producing hashes very quickly and with low collision rates.Hashing is an important Data Structure which is designed to use a special function called the Hash function which is used to map a given value with a particular key for faster access of elements.

The efficiency of mapping depends of the efficiency of the hash function used. If you like GeeksforGeeks and would like to contribute, you can also write an article using contribute. See your article appearing on the GeeksforGeeks main page and help other Geeks. Please write comments if you find anything incorrect, or you want to share more information about the topic discussed above. Skip to content. Basics Easy Intermediate. Hard Misc Quick Links. Non-overlapping sum of two sets Find elements which are present in first array and not in second Check if two arrays are equal or not Pair with given sum and maximum shortest distance from end Pair with given product Set 1 Find if any pair exists Find missing elements of a range k-th missing element in increasing sequence which is not present in a given sequence.

Clone a Binary Tree with Random Pointers Largest subarray with equal number of 0s and 1s Longest subarray having count of 1s one more than count of 0s Longest subarray having count of 1s one more than count of 0s Count Substrings with equal number of 0s, 1s and 2s Print all triplets in sorted array that form AP All unique triplets that sum up to a given value Find all triplets with zero sum Count number of triplets with product equal to given number Count of index pairs with equal elements in an array Palindrome Substring Queries Find smallest range containing elements from k lists Range Queries for Frequencies of array elements Elements to be added so that all elements of a range are present in array Cuckoo Hashing — Worst case O 1 Lookup!

We use cookies to ensure you have the best browsing experience on our website.The canonical reference for building a production grade API with Spring. In Java, efficient hashing algorithms stand behind some of the most popular collections we have available — such as the HashMap for an in-depth look at HashMapfeel free to check this article and the HashSet.

In this article, we'll focus on how hashCode works, how it plays into collections and how to implement it correctly. Java provides a number of data structures for dealing with this issue specifically — for example, several Map interface implementations are hash tables.

When using a hash table, these collections calculate the hash value for a given key using the hashCode method and use this value internally to store the data — so that access operations are much more efficient.

Objects that are equal according to their equals must return the same hash code. It's not required for different objects to return different hash codes. This is typically implemented by converting the internal address of the object into an integer, but this implementation technique is not required by the JavaTM programming language.

The User class provides custom implementations for both equals and hashCode that fully adhere to the respective contracts. Even more, there's nothing illegitimate with having hashCode returning any fixed value. However, this implementation degrades the functionality of hash tables to basically zero, as every object would be stored in the same, single bucket. In this context, a hash table lookup is performed linearly and does not give us any real advantage — more on this in section 7.

Let's improve a little bit the current hashCode implementation by including all fields of the User class so that it can produce different results for unequal objects:. This basic hashing algorithm is definitively much better than the previous one, as it computes the object's hash code by just multiplying the hash codes of the name and email fields and the id. In general terms, we can say that this is a reasonable hashCode implementation, as long as we keep the equals implementation consistent with it.

The better the hashing algorithm that we use to compute hash codes, the better will the performance of hash tables be. While it's essential to understand the roles that hashCode and equals methods play, we don't have to implement them from scratch every time, as most IDEs can generate custom hashCode and equals implementations and since Java 7, we got an Objects.

In addition to the above IDE-based hashCode implementations, it's also possible to automatically generate an efficient implementation, for example using Lombok. In this case, the lombok-maven dependency must be added to pom.

Similarly, if we want Apache Commons Lang's HashCodeBuilder class to generate a hashCode implementation for us, the commons-lang Maven dependency must be included in the pom file:. In general, there's no universal recipe to stick to when it comes to implementing hashCode. We highly recommend reading Joshua Bloch's Effective Javawhich provides a list of thorough guidelines for implementing efficient hashing algorithms.

universal hashing implementation

What can be noticed here is that all those implementations utilize number 31 in some form — this is because 31 has a nice property — its multiplication can be replaced by a bitwise shift which is faster than the standard multiplication:. The intrinsic behavior of hash tables raises up a relevant aspect of these data structures: even with an efficient hashing algorithm, two or more objects might have the same hash code, even if they're unequal.

So, their hash codes would point to the same bucket, even though they would have different hash table keys. This situation is commonly known as a hash collision, and various methodologies exist for handling itwith each one having their pros and cons. Java's HashMap uses the separate chaining method for handling collisions:. In such a case, the hash table is an array of linked lists, and each object with the same hash is appended to the linked list at the bucket index in the array.

Hash function

In the worst case, several buckets would have a linked list bound to it, and the retrieval of an object in the list would be performed linearly. Hash collision methodologies show in a nutshell why it's so important to implement hashCode efficiently. Java 8 brought an interesting enhancement to HashMap implementation — if a bucket size goes beyond the certain threshold, the linked list gets replaced with a tree map.

universal hashing implementation

This allows achieving O logn look up instead of pessimistic O n. To test the functionality of a standard hashCode implementation, let's create a simple Java application that adds some User objects to a HashMap and uses SLF4J for logging a message to the console each time the method is called. The only detail worth stressing here is that each time an object is stored in the hash map and checked with the containsKey method, hashCode is invoked and the computed hash code is printed out to the console:.This looks like a very easy and very efficient way of creating an m bit hash needing only m ands and m shifts.

As this needs to examine each bit to effectively count the number of ones in the data this seems to need m operations. In fact the job can be done in a number of operations that equals the number of bits set.

At first it seems impossibly difficult to do without using shifts and tests to find the first bit set. At this point you might think that no progress has been made because while you have zeroed the least significant set bit you have set other lower order bits. Of course the trick is that the original data already had these bits zeroed. So if you And the new value with the original then the result will have all of those bits zeroed in addition to the least significant set bit. Now you can put this to use in a parity function that only iterates the number of set bits times:.

So in this case we need to generate m bit values to represent the columns - but why bother? It costs the same to generate to generate 32 bit positive values. We can simply truncate the result at the end to m bits and get the same result as if we had truncated the columns to m bits before the calculation.

To avoid interacting with the previous code we can change the constructor to create a second random matrix in column order:. Now the elements of the array, or at least the first m bits are regarded as the columns of the matrix. Now to work out the hash we select the columns that correspond to the bits set in the data and exclusive or them together:.

At the end we truncate the result to m bits by right shifting the result down to leave only m bits. The most obvious improvement is to unroll any fixed sized loop to eliminate the loop structure. A more complex optimization would be to use a very long binary word representation or to use a GPU to parallelize the algorithms. Notice that either algorithm lends itself to being implemented in hardware quite easily. If you need a universal family of hash functions to try out another algorithm then either of the two methods works well.

Random Matrix Hashing. Hashing solves one of the basic problems of computing - finding something that you have stored somewhere. The Bloom Filter. The Invertible Bloom Filter. Storage Mapping Functions.

Grammar and Torture Computational grammar is a subject that is sometimes viewed as a form of torture by computer science students, but understanding something about it really does help Related Articles. Article Index Universal Hashing.