Questions tagged [hashing]
The hashing tag has no usage guidance.
123
questions
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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 ...
1
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1answer
45 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:
...
1
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1answer
56 views
In perfect hashing, why does a secondary hash table that is quadratic in size leads to no collisions?
See below a screenshot from CLRS 3rd Edition (Section 11.5, "Perfect Hashing"). The last sentence of the last paragraph says that the choice of $m_j = n^2_j$ leads to collision-free constant-time ...
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0answers
13 views
At what tier does consistent hashing get implemented?
Where does the code for consistent hashing reside? I have read how it is implemented (at a high level), but am unsure if it is exposed as a microservice between the web server and the app servers or ...
2
votes
3answers
69 views
Building a perfect hashing table
My understanding is that one way to build a perfect hash, as per CLRS, is to use two levels of hashing, with universal hashing functions at each level.
More specifically, CLRS shows that assuming $...
1
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2answers
26 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 $$(...
4
votes
2answers
3k views
simple uniform hashing: unclear definition of probability
I am trying to understand the assumption of Simple Uniform Hashing (SUHA) as e.g., in CLRS textbook; or other courses about hashing.
The usual description given to SUHA is (cf. CLRS):
"we shall ...
1
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1answer
52 views
Universal hash functions - Proof
Problem statement
Let $K$ be a set of keys with $|K| = n$ and define the index set $I = \{0, \ldots, m-1\}$. Now let $H = \{h \mid h : K \to I\}$, i.e. $H$ contains all hash functions which map the ...
1
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1answer
46 views
Using hashing to solve 4-sum problem
The famous 4-sum problem is to find 4 elements at unique indices in an array which sum to a given X. I was looking at one solution I found:
...
0
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0answers
32 views
Quadratic probing in hash tables
I need to construct a hash table with initially $7$ empty entries. Now add $6$ values to the table using the quadratic probing function
$$
s(j,k) = \lceil j/2 \rceil^2 (-1)^j
$$
such that for some ...
1
vote
2answers
176 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
56 views
How does secondary clustering occur in hashing?
One of my friends said me that secondary clustering is the phenomenon occurring when the probe sequence has the same initial value. This definition shows that secondary clustering occurs in linear ...
0
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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 ...
0
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1answer
42 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
29 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
23 views
Space complexity of using a pairwise independent hash family
I'm trying to analyze the space complexity of using the coloring function $f$ which appears in "Colorful Triangle Counting and a MapReduce Implementation", Pagh and Tsourakakis, 2011, https:...
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0answers
32 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, ...
1
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1answer
47 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 $\...
1
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1answer
20 views
Hash function, $h(k) = \lfloor km \rfloor$ is simple uniform for real $k$ independently, uniformly distributed in the range $0 \leq k < 1$
I was going through the text Introduction to Algorithms by Cormen et. al. where I came across the following statement:
If the keys are known to be random real numbers $k$ independently and uniformly ...
1
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0answers
18 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 ...
2
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1answer
66 views
Uniform Hashing. Understanding space occupancy and choice of functions
I'm having troubles understanding two things from some notes about Uniform Hashing.
Here's the copy-pasted part of the notes:
Let us first argue by a counting argument why the uniformity property,
we ...
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0answers
9 views
Analysis of succefull and unsuccefull search in a sorted hash table that resolves collision by chaining
I am trying to solve a problem where we have to analyze the expected time for successful and unsuccessful search in a hash table of $n$ elements and $m$ slots . But the hash table has a property that ...
1
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1answer
29 views
Analysis of Universal Hashing
I was reading universal Hashing from Introduction to Algorithms by Cormen et al., and came across the following corollary regarding search, insert and delete functions on Universally Hashed tables:
...
1
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1answer
37 views
Is there a way to hash a turing machine?
If we have a Turing machine with various $\delta(q_i, a_i) = (q_j, a_j, Direction)$ where Direction can be L or R(denoting the movement of head), can we encode it uniquely to some natural number(which ...
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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
78 views
Suggest how to allocate and deallocate storage for elements within the hash table itself by linking all unused slots into a free list
Suggest how to allocate and deallocate storage for elements within the hash table itself by linking all unused slots into a free list. Assume that one slot can store a flag and either one element plus ...
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0answers
15 views
Describe a procedure that selects a key uniformly at random from among the keys in the hash table and returns it in expected time O(Lā (1+1/Ī±))
This question is from CLRS. The following is what I understand:
The procedure is as follows:
1. First we randomly choose one index in T[m]
2. Let nk denote the number of elements in the chosen slot T[...
4
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0answers
79 views
Expected search times with quadratic vs linear probing
Why exactly does quadratic probing lead to a shorter avg. search time than linear probing?
I fully get that linear probing leads to a higher concentration of used slots in the hash table (i.e. ...
1
vote
1answer
45 views
Bit representation of the hashing multiplication method
In the picture below from CLRS, I fail to understand why exactly $h(k)$ = the $p$ highest-order bits of the lower w-bit half of the product.
For context, this is supposed to compute
$h(k) = \lfloor ...
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1answer
42 views
Universal hashing - insert / search / delete
I don't understand the highlighted text below in CLRS 3rd Ed.:
I'm not sure I even understand what the sentence is trying to say. For example:
What do they mean by "... operations containing $\...
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0answers
27 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 ...
0
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1answer
39 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 ...
0
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1answer
29 views
What is the best of given hashfunctions?
In our exam on algorithms there was a question, where given 3 hashfunctions we had to chose one and explain why it's the best.
h_1(x,i)=(x+5*i) mod 1000
h_2(x,i)=(x+17*i) mod 1000
h_3(x,i)=(x+32*i) ...
3
votes
1answer
774 views
Flajolet-Martin Algorithm : question about use of certain hash functions
this is a question given in a PDF about streaming algorithms (this isnt an assignment but im trying to understand)
Exercise 4.4.1 : Suppose our stream consists of the integers 3, 1, 4,
1, 5, 9, 2,...
7
votes
4answers
16k views
Two-way Hash Functions
While I'm aware most (good) hash functions are one-way (or at least mostly so), I'm wondering if there's any construct (not necessarily called a hash function) which behaves in many ways like a hash ...
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0answers
40 views
Find a non-minimal sequence of elements covering the support set
Consider a sequence $s$ of $n$ integers (let's ignore the specifics of their representation and just suppose we can read, write and compare them in $O(1)$ time with arbitrary positions). Denote $\text{...
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0answers
54 views
Probability of colisson for classes of hash functions
I am going through some old exams in one of my courses, and I don't have access to solutions. I've found a problem which I am not sure how to tackle. I am not looking for the answer but some help/...
0
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2answers
606 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 ...
3
votes
3answers
807 views
Simple Uniform Hashing Assumption and worst-case complexity for hash tables
Is the Simple Uniform Hashing Assumption (SUHA) sufficient to show that the worst-case time complexity of hash table lookups is O(1)?
It says in the Wikipedia article that this assumption implies ...
3
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0answers
267 views
Time complexity of obtaining the set of distinct elements in a sequence?
Consider a sequence $s$ of $n$ integers (let's ignore the specifics of their representation and just suppose we can read, write and compare them in O(1) time with arbitrary positions). What's known ...
2
votes
3answers
2k views
How does Rabin fingerprint finds breakpoints (chunk boundary)?
I was reading up on chunking and found Rabin fingerprinting is also used to break files into chunks. After reading about this algorithm, I understood how rolling hash is computed using Rabin ...
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votes
4answers
193 views
How do you find a hash function that respects a custom equality function?
I've been tasked with hashing arbitrary types in C++, with the caveat that A == B implies hash(A) == hash(B) even if equality of ...
1
vote
2answers
71 views
Is there a running hash algorithm that can efficiently handle arbitrary updates to a file's contents?
This question is about file-hashing/fingerprinting algorithms (similar to SHA-1 and MD5 and so on). Those algorithms are handy ...
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0answers
30 views
Linear probing and tabulation hashing
I'm currently reading the paper "The Power of Simple Tabulation Hashing" by Mihai Patrascu and Mikkel Thorup [1] because I want to adapt the proof of the constant time complexity of linear probing for ...
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0answers
57 views
Structure Preserving Continuous Hash Function
This question was originally posted on super user, but redirected here based on some suggestions.
I am completely new with computer science, and not only recently did I run into the notion of hashing....
2
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1answer
97 views
Given a family of hash functions in table form, how can I know whether it's universal?
I've been given the following two families of hash functions:
H
and
G
Each family has three functions $\{0,1,2,3,4\} \to \{0,1,2\}$ that can be seen in the tables above. For each family I need to ...
1
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0answers
15 views
While computing signature matrix in min hashing, can I take nth row of the permutation P in which document d has value 1?
I am learning about some techniques to find similarity between documents. One of the methods is Min Hashing. According to Min Hashing we can find a signature matrix given a random permutation, P. ...
0
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0answers
34 views
Construction of hash function with a given distribution
Two questions about the construction of a hash function:
Let $U = \{u_1,...,u_n\}$ be a set of size $n$, and suppose that one is interested in a function $h\colon U \rightarrow [0,1]$ such that $h$ "...
3
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1answer
69 views
The expectation of the total number of pairs of keys in a hash table that collide using universal hashing
I am reading CLRS relating to perfect hashing. When computing the
$$
\mathbb{E}[\sum_{j=0}^{m-1}{n_j\choose{2}}]
$$
where $m$ is the number of slots in the hash table, and $n_j$ is the number of keys ...
1
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1answer
385 views
is modulo of hash function is evenly distributed?
if I take the result of a 32bit hash function(the param is random string) and apply module N on the result - will the values be evenly distributed?
so if I have a histogram of values [0,N-1] will the ...
