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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

47
votes
4answers
35k views

Why is it best to use a prime number as a mod in a hashing function?

If I have a list of key values from 1 to 100 and I want to organize them in an array of 11 buckets, I've been taught to form a mod function $$ H = k \bmod \ 11$$ Now all the values will be placed ...
4
votes
1answer
297 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 ...
2
votes
1answer
2k views

How to get expected running time of hash table?

If I have a hash table of 1000 slots, and I have an array of n numbers. I want to check if there are any repeats in the array of n numbers. The best way to do this that I can think of is storing it in ...
17
votes
2answers
5k views

Could quantum computing eventually be used to make modern day hashing trivial to break?

Simply put, if one were to build a quantum computing device with the power of, say, 20 qubits, could such a computer be used to make any kind of modern hashing algorithm useless? Would it even be ...
4
votes
2answers
660 views

Hash size: do prime numbers “near” powers of two are bad?

Cormen et al.'s "Introduction to Algorithms" says the following about the division method hash function $h(k)=k \text{ mod } m$: A prime not too close to an exact power of 2 is often a good choice ...
10
votes
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 ...
4
votes
1answer
1k views

What exactly is a hash function?

I have no idea how I managed to get this far in life without ever really grasping this but as it happens I'm still very confused on the concept of a hash function. I did some googling/wikipedia-ing, ...
2
votes
3answers
283 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 ...
2
votes
1answer
1k views

Finding Hash of Substring [i, j] in O(1) using O(|S|) pre computation

Given a string S of length n characters, is it possible to calculate the Hash of its substring [i, j] (From index i to index j. Inclusive) in O(1) using some form of precomputation ? Maybe a ...
4
votes
0answers
59 views

Is it possible to compute an equality hash for nodes in a *cyclic* directed graph in less than quadratic time?

Calculating hashes for nodes in an acyclic graph is well known using a Merkle tree. With some simplifying assumptions, a simple algorithm will also calculate hashes for nodes in a cyclic graph... but ...
3
votes
1answer
66 views

What are the examples of the easily computable “wild” permutations?

I am looking for the function $y=f(x)$ that would map the integer interval $[0,n)$ into itself $[0,n)$. The function must be bijective, so it is a permutation of n elements. It should "randomize" the ...
3
votes
1answer
242 views

What is an example of a weakly universal hash function that is not pairwise independent?

A family of hash functions $H_w$ is said to be weakly universal if for all $x \ne y$ : $$P_{h \in H_w}(h(x) = h(y)) \leq 1/m$$ Here the function $h:U \rightarrow [m]$ is chosen uniformly from the ...
2
votes
3answers
1k 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 ...
2
votes
1answer
638 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 ...
2
votes
3answers
434 views

Which fingerprinting/hashing algorithms support compounding?

The definition of fingerprinting algorithms in Wikipedia describe a property called compounding as you can see here as: Some fingerprinting algorithms allow the fingerprint of a composite file to ...
2
votes
1answer
1k views

Find similar vector by Locality Sensitive Hashing

I have many vectors in my database. They are in high dimensions such as: $v_1$ : $\langle 23, 23, 1, 33, 103, 219, \dots \rangle$ $v_2$ : $\langle 92, 83, 1, 33, 239, 192, \dots \rangle$ ... I will ...
1
vote
0answers
76 views

Bloom filters vs storing hashes as numbers

In competitive programming there is a trick for storing a set of strings(or objects really) to reduce memory - you only keep the hashes of the strings in a hash-table (usually as 32 or 64 bit integers)...
0
votes
0answers
189 views

How does hashing achieve sketching?

Given a sequence $x \in \{ 1,2,3...,\vert \Sigma \vert \}^*$ one wants to create a sketch of it say $s(x)$ of size $\frac{2c}{3}k (ln^2 k)$ bits. And that seems to be achieved as follows, pick at ...