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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How 'Avalanche Effect' got its name?
I wonder how or why Avalanche Effect got its name.
Avalanche Effect is a desirable property of cryptographic algorithms, wherein if an input is changed slightly (...
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39 views
Why mod operation can be used as hash function
I'm new here, and I'm currently trying to understand why mod operation can be used as a hash function.
For example, consider the function $h(x)=x\mod 2^{256}$, where $x$ can be a string of any length. ...
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1answer
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How to show independence and uniform distribution of hash codes from k-wise independent hash functions?
Most definitions of a $k$-wise independent family of hash functions I have encountered state that a family $H$ of hash functions from $D$ to $R$ is k-wise independent if for all distinct $x_1, x_2,\...
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1answer
52 views
How can I prove or disprove that the following function is bijection?
For a research project, I tried to prove or disprove that a function called xxhash128_low is a bijection from 64 bit unsigned integer to 64 bit unsigned integer. I have shown that it is sufficient to ...
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Integer set disjointness query on sketches with something like homomorphic hashing
Suppose I have two sets of integers $A$ and $B$ and I have a sketch data structure described by a function $\mathsf{sketch}_n : \mathcal{P}(\mathbb{Z}) \to 2^n$ that returns a bitstring of size $n$. ...
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Question regarding the proof that quadratic probing always finds an empty slot if the table is less than half full
to prove this statement I assume the probing function as: $$h(i,x)=h'(x)+i^2 \text{ mod t} $$
And for $0\leq i,j < \frac{t}{2}$; $i\neq j; t \text{ prime}$: $$h(i,x) = h(j,x)$$
This results into $$(...
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63 views
Universal hash functions - Proof
Problem statement
Let $K$ be a set of keys with $|K| = n$ and define the index set $I = \{0, \ldots, m-1\}$. Now let $H = \{h \mid h : K \to I\}$, i.e. $H$ contains all hash functions which map the ...
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Bad data for hash function
Is it possible to choose such a nontrivial set of queries so that the amortized running time for a hash table with a public key and a function like $(a_{N ā 1}k^{N ā 1} +... + A_{1}k + a_0) (mod \: p)$...
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1answer
27 views
Why is this implementation of the hash function bad?
I have a task of hashing DNA sequences. Let the DNA be long sequences of four amino acids, which we will denote by the letters $A, T, G$ and $C$.
My hash function $h$ take DNA as an input and return ...
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2answers
126 views
Store a n-bit string using only O(log n) space
Is it possible to somehow store a $n$ bit string using only $\mathcal{O}(\log{n})$ space? I am thinking if the string could be stored using a hash function, but I am not sure if it is even possible.
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Is there a standard name for this property of hash functions?
A hash function $H$ operating on strings can have the following property:
Let $x$ be a string and $c$ a character. Given $H(x \cdot c)$ and $c$,
$H(x)$ can be determined uniquely (where $\cdot$ stands ...
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1answer
18 views
Choosing the right function
I'm trying to hash integers n = 4k(0,4,8,12,16...) into an array of linked lists of size 4 (chaining).
What is a good hasing function that guarantees a good ...
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1answer
44 views
oone exmple in hash topics?
Example: Suppose $H:${$1,...,n$} $\rightarrow ${$1,..,n$} be a uniform hash function. for input $x$, $z$ is equal to number of trailing zero in the right side of $H(x)$. for $0 \leq c \leq 1$ what is ...
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30 views
Minimal perfect hash function for set of integers
This might be a trivial question, but I have the following problem: I want to (perfectly) hash a number of lists of integers of length $n$, with all entries between $k_{min}$ and $k_{max}$. How can I ...
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52 views
Pairwise independent hash function family?
I am looking for a family of pairwise independent hash functions $\mathcal{H} = \{h \mid h:[n]\rightarrow [m]\}$ that is easily computable.
As an example that doesn't seem to work, choose a prime $p &...
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1answer
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Clarification on evenly dispersing modular hashing [duplicate]
I'm going over "Algorithms fourth edition" by Robert Sedgewick and Kevin Wayne.
In the chapter on hash tables I have encountered an easy hashing method called "modular hashing"
<...
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21 views
Expected runtime for hashing with a binary search tree as collision handling
I thought about implementing a data structure with expected runtime of O(1) for insertion, deletion and look-up and a worst case runtime for these operations of O(log(n)). This is under the assumption ...
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37 views
Simple incremental hash funcion
I have permutations:
4 1 2 5 3
4 3 2 5 1
numbers can be order magnitude of 1000 (fits in two bytes)
I want compute 32 bit (or better 64 bit) hashes, it should be ...
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1answer
73 views
What is Simple Uniform Hashing, and why searching a hashtable has complexity Ī(n) in the worst case
Can anyone explain nicely what Simple Uniform Hashing is, and why searching a hashtable has complexity Ī(n) in the worst case if we donāt have uniform hashing (where n is the number of elements in the ...
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23 views
Double Hash Family Universality
Here I am given 2 hash families and I need to prove the universality of the double hash, but I am stuck as to how to prove this. I know the properties of an epsilon-universal family is that the ...
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1answer
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When and Why do I Rehash?
I am studying hashing and reading the part of universal hashing. I have read that I want to draw a hash function from universal hash families when I rehash. When and why do I rehash?
One reason to ...
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1answer
57 views
Merkle tree sorting leaves and pairs
I am implementing a Merkle tree and am considering using either of the two options.
The first one is sorting only by leaves. This one makes sense to me since you would like to have the same input ...
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33 views
In Universal Hashing- probability of poor performance is small and is the same for any set of keys of the same size
I was going through the text Introduction to Algorithms by Cormen et. al. where I came across the following claim:
Universal Hashing uses randomization.For the example of a compiler's symbol table, ...
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1answer
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Difficulty in understanding few steps in the proof: “The class $\mathscr{H}_{p,m}$ of hash functions is universal”
I was going through the text Introduction to Algorithms by Cormen et. al. where I came across the following excerpt regarding the said proof and the steps where I felt difficulty are marked with $\...
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1answer
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Proving that the two definitions of Universal Class of Hash Function are equivalent (as dealt with in CLRS)
I was going throught the text Introduction to Algorithm by Cormen et. al. where I came across the two alternative definitions of Universal Class of Hash Function.
The versions are as follows:
...
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21 views
In Hashing-collison resolved by chaining: Intuition behind $O(1) + \alpha= \Theta(1+\alpha)=O(1)+1+\frac{\alpha}{2}-\frac{\alpha}{2n}$
Hashing-collison resolved by chaining: $O(1) + \alpha= \Theta(1+\alpha)=O(1)+1+\frac{\alpha}{2}-\frac{\alpha}{2n}$
I was going through the text Introduction to Algorithms by Cormen et. al. and in the ...
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2answers
205 views
Double Hashing with Strings as key
How would you choose the second hash function with for double hashing with string as key?
My first hash function is the scalar product of a random int array with the 16 bit number of each char. Is ...
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61 views
Variance of chain length in hashtable
I have a hashtable with length $m$. Initially it's empty. Next, $n/2$ unique random numbers $\in [0, n]$ are added to it.
What would be variance of chain length when such $n/2$ numbers are being added ...
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Is this example in Skiena's Algorithm Design Manual correct?
i think the above is incorrect; specifically, i think H isn't bijective. say our alphabet is the lowercase letters [a-z] and ...
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Size of order-preserving minimal perfect hash family
Suppose we have a universe of $u=|U|$ elements. We called a set of $H$ function $(U,m)$ order-preserving minimal perfect hash family (OPMPHF) if for every subset $M\subset U$ of size $m$ has at ...
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101 views
What is the best hash functions for millions of String keys?
I have a situation where there are a million Keys of type String and I want to use the Symbol table to store the key and the value.
The problem that the retrieval process is too slow and I want to ...
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2answers
40 views
Theoretical question about Zobrist hashing and chances of collision with slight modification
I have a hash table that uses zobrist hashing to calculate the hash for various positions. The hash table is used to look up various transpositions. For some positions I do not want to allow any ...
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45 views
Hashing algorithm which minimizes distribution
Consider applications A1, A2 .. AN having properties P11, P12,... PN1, PN2.. Also consider buckets ...
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1answer
61 views
How to generate, validate, and invalidate a set/list of numbers in O(1) time and space?
Imagine my server is generating "tokens" of some sort for a client on a regular basis. When a client asks for a token, the server responds with a new value (and any other supplemental information it ...
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2answers
58 views
Rolling hash hacking
The hash value of a string $s$ is given by
$$
h(s) = \sum^{|s|}_{i = 1} s_i \cdot p^{|s| - i} \mod m; \text{ $m$ is prime, $m < 10^{12}$}.
$$
The string $s$, $p$, $m$ is given,
$|s| \le 14$, ...
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1answer
225 views
Separate Chaining hashing: time complexity of successful search
In a simple uniform hashing with chaining collision, the time complexity of a successful search is: $Ī(1 + (1 + \frac{Ī±}{2} - \frac{Ī±}{2n}))$ where $Ī±=\frac{n}{m}$, but I don't understand how to ...
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Formal definition of hash function
I was reading through the classic CLRS with the intention of reviewing the hash tables theory, more specifically the hash function definition I just wanted a reference to quote.
I cannot find a ...
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28 views
How to generate unique keys for different two dimensional matrices having different sizes?
No. of rows in the table (as given in image) is not known beforehand . The problem I am dealing with generates different 2-D matrices based on the input data given. As soon as a matrix generates it ...
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29 views
Protecting a specific sized message with some limitations
So I make a research on my own. I have a device it allows a 64bit message. I wanted to secure it but I 64bits arent just enough to hash it and encrypt it. Is there really any good Hash function out ...
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23 views
Hashfunction for unique character distributions
The original problem is given a large input file, with n input lines of random string, find the number of pairs-> meaning same number and type of characters, in the file. Constraint on type of ...
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1answer
101 views
generalizing ball-bin problem to k-universal family
I am trying to solve a question in the book on Probability and Computing by Michael Mitzenmacher, Eli Upfal. The question asks to generalize ball-bin problem for 2-universal hashing to $k$-universal ...
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1answer
41 views
Primary clusting in linear probing coliision resolution: there can only be one cluster/block, right?
I believe primary clustering is a problem with the linear probing method of hash collision resolution. But the description makes it sound like there can be multiple clusters of contiguous blocks. I ...
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Looking for memory-efficient way to detect hash collisions
Given a hash function H, it's possible that H(a) = H(b) = c
Let's assume we have a big data set [N1 ... Nk], with K items and we hash each item in this set
After operation is done, we'd get a set of ...
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1answer
57 views
Efficiently extendable hash function?
I'm wondering whether there exist any good hash functions with the following property: Assume that $x$ is some string over some alphabet $A$, then given $H(x)$ we can compute in $O(1)$ time both $H(ax)...
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1answer
109 views
Choosing an independent hash function, given hash function value
Supposed we have a function $h:U\to [m_1]$. Given this hash function, can we generate without using randomization or a universal hash collection another hash $h':U \to [m_2]$, which depends on $h$ ...
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32 views
Pairwise hash functions that are independent from each other
Is there there a way to build a collection of universal hash functions $H=\{h| h:U\to D \}$ where the values of two hash functions are independent one from another? i.e., $\Pr_{h_1,h_2\in H}(h_1(x)=y ...
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690 views
Hash function to return only positive number from integer
What would be a good hash function that will return a positive integer value, even if the key is an negative integer value? How do I pick a hash function? So what I would want is to associate negative ...
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Are hash functions one-way?
I have heard that we can convert any text to hash code , but hash code can't be converted back to text without brute force.
Suppose we consider the text "mal". The hash codes of the ...
