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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1answer
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Hashing using Horner’s Rule
When hashing a (key, value) pair where the key is a string, I have seen the following hash function in use:
E.g. $c_n + 256c_{n-1}+ 256^2c_{n-2}+...256^{n-1}c_1$, where this represents the string $...
2
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0answers
18 views
Does there exist a locality sensitive hashing for $\ell_p$-norm distance where $p>2$?
It is well known that the $p$-stable distribution can be used to generate locality sensitive hash code for $\ell_p$-norm distance measure where $p \le 2$. However, it seems that the situation for $p&...
0
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1answer
13 views
Detecting and correcting collisions in (Zorbist) hashing to avoid errors in transposition table
Context
Say I have a transposition table that uses keys produced by (e.g. Zorbist) hashing game positions.
The table has a finite recycled memory (key % p is the <...
1
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1answer
30 views
Avoid Storing Keys in Key-Value Store by Replacing the Key with 128-bit Murmur3 Hash
I want to develop LRU key-value data store and in that wanted to get rid of space to store the key itself. Instead wanted to store a 128 bit murmur hash. The structure of data-store that I want to ...
4
votes
1answer
147 views
Count Sketch probability bound
I have been reading up on the Count Sketch algorithm, and I stumpled upon the Count Sketh algorithm explained in section 5 of https://www.cs.dartmouth.edu/~ac/Teach/data-streams-lecnotes.pdf. Then, I ...
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1answer
14 views
Universal hash function for strings of unbounded length
Is there a (weakly) universal hash function for strings without any assumption of the string length?
I did not find one on Google / Wikipedia.
2
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0answers
29 views
Finding the longest power subsequence
A power sequence is a sequence containing consecutive powers of a number starting from power one. for example $3^1, 3^2, 3^3$ is a power sequence. The question is to find the length of the longest ...
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16 views
Propose a family of hash functions with $mod p^2$ for some prime number $p$
I need to define a family H of universal functions $\{0,1, ..., p^k−1\} →\{0,1, ..., p^2−1\}$.
Now based on a similar example I was thinking of something like:
Given some $a= (a1, a2, ..., ak)∈\{0, ......
0
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1answer
65 views
Shuffling Bits For Uniform Distribution
I am writing a hashing algorithm to be used in the key-value data store. That is for each key the location of the data is determined. The structure of the data store is given a key, a value needs to ...
0
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0answers
18 views
Hash tables for storing data in an application that supports partial search
Is a hash table a good data structure for storing data in an application that support partial search such as "select * from MyTable where name like 'John%'. If not, what is?
I would have thought ...
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0answers
21 views
What is the order of magnitude of bitwise operations involved in a SHA-256 hash?
Specifically, how many bitwise operations (approximately, could be just order of magnitude) occur each time a Bitcoin ASIC miner performs a SHA-256 hash in typical mining computation, i.e. as it ...
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21 views
If the load factor is a decimal (say 3.6), what is the length of each chain in a hash table that utilizes separate chaining?
I understand that if the load factor were 2, then the length of the chain would be 2 for each index in the array, but what happens if the load factor is a decimal? Do we round up or down?
2
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1answer
108 views
Constructing 2-Universal Families
Let H be a class of all functions, mapping M possible keys to N integers. Is it true that H is a 2-universal family? Is it a good idea to use H in applications?
I don't even know where and how to ...
1
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1answer
48 views
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 (...
1
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1answer
45 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. ...
1
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1answer
38 views
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,\...
1
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1answer
58 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 ...
4
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3answers
89 views
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 $n$. ...
1
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2answers
53 views
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 $$(...
1
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1answer
106 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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0answers
19 views
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 − 1}k^{N − 1} +... + A_{1}k + a_0) (mod \: p)$...
0
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1answer
30 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 ...
1
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2answers
136 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 ...
0
votes
1answer
19 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 ...
0
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1answer
45 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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0answers
34 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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0answers
66 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 &...
1
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1answer
18 views
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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0answers
24 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 ...
0
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0answers
42 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
81 views
What is Simple Uniform Hashing, and why searching a hashtable has complexity Θ(n) in the worst case
Can anyone explain nicely what Simple Uniform Hashing is, and why searching a hashtable has complexity Θ(n) in the worst case if we don’t have uniform hashing (where n is the number of elements in the ...
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0answers
25 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
108 views
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 ...
4
votes
3answers
107 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 ...
2
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0answers
39 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, ...
0
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1answer
66 views
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 $\...
0
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1answer
82 views
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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2answers
345 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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0answers
68 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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0answers
29 views
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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2answers
38 views
1
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1answer
34 views
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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4answers
198 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
52 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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0answers
45 views
Hashing algorithm which minimizes distribution
Consider applications A1, A2 .. AN having properties P11, P12,... PN1, PN2.. Also consider buckets ...
3
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1answer
85 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 ...
2
votes
2answers
64 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,
$|s| \le 14$, ...
0
votes
1answer
396 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: $Θ(1 + (1 + \frac{α}{2} - \frac{α}{2n}))$ where $α=\frac{n}{m}$, but I don't understand how to ...
0
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1answer
56 views
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 ...
