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Questions tagged [hash]

Mathematical function that maps arbitrarily-sized data to fixed-size integers, often used as keys in hash tables or to help ensure data integrity

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are these functions for open address hashing, proper?

I want to use these two functions in two hash-tables with open-addressing. Is there any problems with these functions? If yes, why they are not appropriate? ...
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70 views

Can we recognize the difference of two strings of $2^n$ length using polynomial size strings?

Is it possible to transform binary strings of length $2^n$ to $n^c$ binary strings of sized $n^d$ such that $$\forall s_1,s_2 \; \exists i \in \{1,\cdots,n^c\} \; f_i(s_1)\neq f_i(s_2),$$ Where two ...
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72 views

Hashing methods for validating dowloaded files

The standard algorithm to generate hashes of files which are downloaded is MD5. For example, when ISO files of Linux distributions are offered most of the time they also give the MD5 sum so that you ...
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1answer
236 views

Using random projections for locally sensitive hashing

I recently came to see that this library sparselsh uses random projection to perform locally sensitive hashing of documents. The proof is such that based on cosine similarity to the vector. In other ...
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1answer
112 views

How to extend a hash function to manipulate longer integers?

Carter and Wegman introduced in the paper Universal Classes of Hash Functions the $H_{1}$ universal class of hash function. This is essentially the function $h_{a,b}(x) = ((a\cdot x+b)\mod p)\mod m$. ...
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2answers
3k views

Check-digit algorithm that includes characters?

I have a data set that uses a very simple modulo 10 checksum algorithm which ignores alphabetic characters entirely. Which wasn't a big deal, as the few alphabetic characters present weren't ...
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102 views

Perfect hashing function algorithm

Is there a good (perfect) hashing algorithm for the following problem? We have $n \ll m$ (say $n=150$ and $m=5\times 10^{12}$) and we want a hash table to store integers up to $m$ whose prime ...
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1answer
2k views

How would you prove a family of functions is universal?

A set of functions from a universe U of keys to n buckets is universal if for every pair of keys in U, say x and y, such that x != y, the probability of h(x) = h(y) is less than or equal to 1/n, for a ...
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614 views

Understanding of hash tables

I am currently studying hash tables in an introductory course to computer science. I was taught that hash table is a data structure that associates a key to an index (a hash table) and then to the ...
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1answer
50 views

Repeated fingerprinting after array updates

I've got a microprocessor and want to quickly identify the settings of my application (stored in some eeprom regions) via a fingerprint instead of having to dump the entire memory every time. So I ...
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1answer
496 views

What is the complexity class of solving hash decision problems?

With $hash_n$, I mean a standard cryptographic hash like sha256, scaled up to have arbitrary length $n$ of its output with the same underlying principles. What is the time complexity class of the ...
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2answers
142 views

Hash functions producing uniform outputs

I've seen this question in a past exam paper, and I know that the answer given is (b), but I'm not sure why. Which one of the following hash functions on integers will distribute keys most ...
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270 views

Given a string, is it possible to determine which hashing algorithm has produced it, if any?

Given a string, is it possible to determine which hashing algorithm has produced it, if any? For example, the MD5 hash of "string" is b45cffe084dd3d20d928bee85e7b0f21. Is it possible to determine ...
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3answers
2k views

Hash function to hash 6-digit positive integers

Let UID denote a unique identifier. UID's are represented as 6-digit positive integers. I want to insert a collection of UID's in a hash table with $M$ buckets, where $M$ is a prime number (for ...
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1answer
154 views

Do cryptographic hash function solve clustering problems with linear probing?

I understand in open addressing hash tables some clustering will always happen just by random chance, even if the input data is perfectly random, leading to some "best possible" lookup performance hit ...
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2answers
76 views

Information on Tavori and Dreizin ranged hash function?

While doing some digging around in the GNU implementation of the C++ standard library I came across a section in bits/hashtabe.h that refers to a hash function "in ...
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1answer
117 views

Reading CLRS analysis of hashing with chaining

I'm currently reading an analysis hashing with chaining, and it goes over two examples: In the first, the search is unsuccessful; no element in the table has key k. In the second, the search ...
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1answer
1k views

Locality-sensitive hashing random projection

I'm trying to understand how the LSH works for Cosine Similarity metric. For instance, let's say you have $\vec{v} \in \mathbb{R}^d$ and the random vectors $\vec{r_{i}} \sim \mathcal{N}(0, 1)^d$ that ...
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2answers
2k views

Graph adjacency using Hashing

Consider a graph $G = (V,E)$ and the following operation $\text{neighbour}(v_1,v_2)$: returns true if the vertices $v_1$ and $v_2$ are adjacent, and ...
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1answer
1k views

How can one find an element in a Merkle tree?

How can one find an element in a Merkle tree, as effectively as possible? Each internal node has a hash value. So I think, first, hash the value to find, and if an internal node has the same value ...
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1answer
844 views

Hash multiple integers directly using FNV-1a

An alternative version of FNV-1a hash spread on the internet, which operates directly on integers instead of bytes. The offset basis and prime are the same used in the original version, which operates ...
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1answer
653 views

Embedding high dimensional vectors into low dimensional space preserving similarity

I have a collection of high dimensional vectors such as $\vec{a}_{i} \in \mathbb{R}^{n}$ where $n$ is 3000. What I want to do is to embed these vectors into a space such as $\vec{b}_{i} \in [0, 255]^{...
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1answer
232 views

Hash for verifying both compressed and uncompressed data?

Is it possible to have a single hash function output simultaneously verify a compressed block of data as well as its uncompressed counterpart? Trivially one could just use a hash function twice (once ...
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1answer
216 views

Choosing a non-cryptographic hash function for language with no unsigned integers

I'm implementing a hash table in pure UnrealScript, which only has support for signed 32-bit integers. This means no 64-bit integers and no unsigned integers. I was in the middle of implementing an ...
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2answers
199 views

Constraint on Universal set of hash functions

I was reading hashing from CLRS. In it author says: Let $\mathscr{H}$ be a finite collection of hash functions that map a given universe $U$ of keys into the range ${0,1,...,m-1}$. Such a ...
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25 views

How to ensure that no manipulation to data records has been made

Let's say I have a transaction history, like this: Transaction #1: Add 5 Transaction #2: Add 8 Transaction #3: Remove 2 Transaction #4: Cancel Transaction #2 Is ...
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2answers
272 views

What Exactly Does the Term “Key” Mean with Regards to a Hash Table?

I know it is supposed to be some arbitrary term that is a stand-in for a large class of possible objects. But I still don't understand what part of the array the term "key" is meant to represent or ...
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368 views

Mean and variance of number of buckets of length $i$ in hashing with chaining

Consider a hash table with $m$ buckets, with chaining as collision resolution policy. Given the set $S$ that will be stored in the hash table, let $X_i$ be the number of buckets whose chain length is $...
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1answer
568 views

Hash function which is invariant under small changes

I am looking for a hash function which is invariant under small changes. E.g., if I have two strings MyString and MySttring ...
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1answer
52 views

Is this some kind of hashing?

Say I have $n$ vectors $\{ z_i \in \mathbb{R}^D\}_{i=1}^n$ (where $n$ is very large and hence I can't do any calculation which scales as $n$) and I want to create $n$ vectors $\{x_i \in \mathbb{R}^d \}...
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2answers
72 views

Simple pseudorandom split of data

I want to split my data into $n$ approximately equal parts. Which simple hash functions will ensure that the number of $x$ with $h(x)\equiv i\pmod{n}$ is approximately equal for each $i$?
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218 views

Two definitions of universal hash functions

I have seen two definitions of universal hash functions in the literature. For any $i \geqslant 2$ let $[i]=\{1,\ldots,i\}$. Definition 1: A family $\mathcal H$ of hash functions from $[n]$ to ...
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1answer
601 views

Does hashing under the Simple Uniform Hashing Assumption battle worst-case adversaries the same way quick sort does?

One common way for algorithms to battle adversarial inputs is by acting randomly. One popular example is quicksort and choosing pivots randomly (this sort of notions is explained well in section 5.3 ...
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1answer
172 views

Different probabilistic statement for Simple Uniform Hashing

Let me denote the number of elements with $n$ and the size of the table with $m$. I was trying to understand the Simple Uniform Hashing assumption that people and books describe in works and make them ...
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3answers
761 views

What is the formal analysis with Simple Uniform Hashing that the load factor is $\alpha = \frac{n}{m}$

Recall the definition of the load factor is the average number of elements in a chain for hashing for a table $T$ of size $m$ (with $n$ elements in consideration). Let $n_j = T[j]$ be the size of the ...
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862 views

Building static hash table with particular collisions

Is there efficient algorithm to encode keys in hash function with provided collisions? By efficient I mean with low-ish runtime of lookup operation (taking constants into account) and realistic time ...
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1answer
1k views

Understanding Murmur3

The Bloom filter data structure requires a set of hashing functions. The Murmur3 family is a great fit, as it contains the seed parameter to easily create a variety ...
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3answers
2k views

Why is a (collision-less) hashtable lookup really O(1)?

Disclaimer: I know there are similar sounding questions already here and on Stackoverflow. But they are all about collisions, which is not what I am asking for. My question is: why is collision-less ...
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332 views

1-to-1 cryptographically secure bit shuffling

Given an input item (N bytes), I'm looking for a function that will map this to an output (still N bytes). The function should have the following qualities: It should be 1-to-1 so that all inputs ...
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2answers
193 views

Is the following intuition valid for understanding $k$-wise independent hash functions?

I really enjoy reading up on algorithms and data structures and in the course of doing so often come across ones that rely on $k$-wise independent families of hash functions. I'm perfectly comfortable ...
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What is the difference between O(n^2) and O(N)[N*O(1)]?

I was reading this article on gperf. In it they claim that the use of nested if statements for parsing command line input of $N$ options ends up making $O(N^2)$ ...
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857 views

Hash Table: How to Calculate Max Load of a Bucket in Practice

My question is related to this question I posted in math forum: https://math.stackexchange.com/questions/1512644/balls-and-bins-hash-table-a-concrete-example but I could not get an answer that I ...
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4answers
1k views

General theory on Hash Functions?

I'm a computer engineer and I've met hash functions theoretically speaking in "algorithms and data structure" and then in several applications (like databases, operating systems, computer architecture ...
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373 views

Hash-Table in Practice

I have a set of $n$ values,$v_i$ and want to insert them into a hash-table, $HT$, in a way that each bucket (or hash-table cell) has at most $d$ values. I set $k=\frac{n }{d}$, where $k$ is the number ...
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86 views

How to design Hash Functions for the problem of Set Intersection?

This is a specific question about [1]. Before the question, I must explain and organize some topics: 1) In section 3.2, during the "Pre-processing Stage", a hash function maps an element to a bit-...
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2answers
2k views

Why does this particular hashCode function help decrease collisions?

I just read in Effective Java about the hashCode method: Store some constant nonzero value, say, 17, in an int variable called result. For each significant ...
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1answer
201 views

Collisions in independent hashing

Let $H$ be a $s$-wise independent family of hash functions from $\{1,\ldots,M\}$ to $\{1,\ldots,N\}$. It is easy to bound one collision, but are there good bounds for muliple collision ?
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957 views

Finding similar high dimensional real vectors

I have a collection of vectors $v_1,v_2\in [0,1]^n$ and I want to find similar pairs quickly. For similarity, I want to use the Euclidean distance metric $L: [0,1]^n \times [0,1]^n \longrightarrow R$. ...
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Prior papers on hash walks [closed]

Random walks are well known from probability theory. I have the idea for hash walks. If h(x) is a hash function and a,b,c,d,e,f is a boolean sequence then the sort of hash walk I am talking about is ...
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601 views

How would you implement truly random hash functions in practice?

Suppose that $[U] = [0,...,U-1]$ is the universe from which all elements will be taken, and $A$ a hash table of size $m$. A hash function $h:[U]\rightarrow[m]$ is truly random if For any set of ...