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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Simple Uniform Hashing Assumption and worst-case complexity for hash tables
My question: Is the Simple Uniform Hashing Assumption (SUHA) sufficient to show that the worst-case amortized time complexity of hash table lookups is O(1)?
It says in the Wikipedia article that this ...
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2answers
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Universal hashing function probability
Can somebody explain the following:
U is a universe of keys, and H is a finite collection of hash functions mapping U to {0, 1, … , m-1}.
I do not understand definition 2, and thus why amount of ...
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Is there a good way to hash abstract binding trees?
The hash function should be invariant under alpha-renaming. Using de Bruijn notation seems to be possible, but it requires alpha-converting the whole tree when a binding is created, and has the ...
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29 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 $h$ "...
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55 views
Fast hash function for set equality
I'm searching an hash function for integer set equality that must be fast.
It must support update (adding an element already in the set must not change the hash) and union.
MinHash has these 2 ...
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1answer
20 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 ...
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16 views
Time complexity of website access analysis using Hash Tables
I would like to calculate the time complexity of an algorithm which returns the number of accesses of a website and the number of different users who entered. Each user is represented by a unique ...
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1answer
44 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 ...
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1answer
62 views
Prove the probability of which a hash function is collision-free
Suppose $H = \{h_1, ..., h_T\}$ be a family of pairwise independent hash functions mapping $\{0, 1\}^n$ to $\{0, 1\}^{n/2}$. Let $M = \frac{2^{n/4}}{10}$ and let $x_1, ..., x_M$ be any M distinct ...
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1answer
61 views
are they any implications if i reduce a sha256 result into 248 bits?
i am working a prototype using some cryptographic properties.
the question is simple but perhaps deep enough for me to decide :
sha256 is a strong hash function, but i have space for 248 bits only.
...
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1answer
33 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 ...
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1answer
72 views
Indexing Edge Permutations for the Rubik's Cube
I'm working on a Rubik's Cube solver that implements Korf's algorithm, as published in his 1997 paper, Finding Optimal Solutions to Rubik's Cube Using Pattern Databases. His method involves creating ...
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1answer
116 views
Compute hash value according to multiplication method
In "Introduction to Algorithms" by C. E. Leiserson, R. L. Rivest and C. Stein (ISBN: 978-0262033848), p. 264 they state this:
I get everything but the last part stating $h(k) = 67$
...
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1answer
45 views
Reversible Merge of Integer Hash Values
Context:
I am working with a tree-like data structure. I would like every node in the tree to have an integer hash value that is the result of combining the integer hash values for the node's ...
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2answers
52 views
Hash function orders ships from closest to furthest from the origin
Suppose we have a circular radar that scans for ships in an area enclosed by $x^2+y^2 \leq z^2$ (a circle).
We wish to design a hash function $h$ such that, we can order the $n$ ships from closest to ...
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2answers
29 views
O(B) algorithm to find positions of all permutations of smaller string in a bigger string with length B - how is this possible?
Context: I've been working through Cracking the Code Interview and on page 70 the book asserts that there is a O(B) solution to this problem.
If
s = little string and S = len(s)
b = big string and ...
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0answers
25 views
Search operation in hash table
Suppose that we have a hash table of some size $s$ and we have a set of keys $K$. We decide to hash the keys using chaining.
Now assume that we randomly select $k \in \mathbb{N}$ keys from $K$ and ...
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What's the problem with deletion in FKS perfect hashing?
In FKS perfect hashing we construct two levels of tables. To lookup an element we first check in the first table which points us to the correct second level table that will contain the element if it ...
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1answer
50 views
Small space hash functions that are weakly but not strongly universal
This is a follow up to this this question about weakly universal hash functions
A family of hash functions $H_w$ is said to be weakly universal if for all $x \ne y$ :
$$P_{h \in H_w}(h(x) = h(y)) \...
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1answer
269 views
What is an example of a weakly universal hash function that is not pairwise independent?
A family of hash functions $H_w$ is said to be weakly universal if for all $x \ne y$ :
$$P_{h \in H_w}(h(x) = h(y)) \leq 1/m$$
Here the function $h:U \rightarrow [m]$ is chosen uniformly from the ...
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What is a minimal, pseudo-random hash function?
I want to generate pseudo-random hashes of inputs in a way that is optimally time and space efficient.
I'm not at all concerned about security. The output should be evenly distributed and appear ...
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1answer
84 views
Hash table open addressing without dummy
If a hash table is using open addressing as the collision resolution strategy, then during deletion, we mark that slot as dummy.
I understand the reason behind ...
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1answer
69 views
My professor claims that inserting the same key into a hash table again will lead to a collision … – Is he really right?
My whole life I thought
a collision is a situation that occurs when two distinct pieces of data have the same hash value.
Everything looks a little bit different now: A few days ago we had to ...
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1answer
76 views
Fixed point of hash
Are hashing algorithms constructed to guarantee that no fixed point exists?
My assumption is not, because I don’t see what utility that would have. (Please correct me if I’m wrong.) As such, purely ...
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Adaptive radix tree for storing Hash vs HAMT
Is there any disadvantage to using Adaptive radix tree to store hash of key like it is done in HAMT and Ctrie
Would it be slower?
Would it use more memory?
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2answers
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probability of collision
my data's range is from 1 to 9 and I have two subsets of integers from this range.
the hash function takes each of this subsets and calculate product of these three integers and maps this set to the ...
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3answers
1k views
What is the point in hashing a value?
I apologise if this is not the right place for this question... I didn't want to ask on Stackoverflow or CodeReview as it will closed in minutes as "too broad".
A client of mine is writing an API ...
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1answer
36 views
Most efficient way to check if key exist on a table
Imagine a person called Albert. Albert lives in Europe and would love to move to America. One day he got his wish come true. A person called Margareta gave him a key. The value of the key is the same ...
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1answer
58 views
Finding duplicates in a stream of numbers
This is an interview question.
Say you have a function foo() which returns some integer.
You need to write an algorithm that does the following:
(...
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1answer
108 views
In most locality sensitive hashing implemensions of SimHash, why is the cosine distance used and not the euclidean distance?
In Chapter 3 of Mining of Massive Datasets, the basis of locality sensitive hashing is explained. They notably mention simhash for the cosine distance, where random hyperplanes are generated, and for ...
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1answer
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Are hash functions really quantum resistant for commitment schemes?
It is commonly stated that hash functions remain secure in a post quantum world, the justification being that a quantum computer only has the advantage of Grover's search to give it a quadratic ...
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1answer
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Do not understand a concept in analysis of open-address hashing
I am reading the "Introduction to Algorithms" by Thomas Cormen et al. Particularly the theorem which says that given an open-address hash table with load factor α=n/m<1, the expected number of ...
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1answer
312 views
How is this the expected number of of probes in open-address hashing?
I am reading the "Introduction to Algorithms" by Thomas Cormen et al. Particularly the theorem which says that given an open-address hash table with load factor $\alpha = n/m < 1$, the expected ...
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2answers
48 views
Why can't hash coding be reversed?
Why is it impossible to reverse a hash code? There could be some way to crack this coding?
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1answer
275 views
Can we do 4-sum algorithm in O(n^2)?
this is related to the following question:
Generalised 3SUM (k-SUM) problem?
Without loss of generality, let's only consider even $k$, or just $k=4$.
My question is, after summing all pairs of ...
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1answer
57 views
Does this excerpt from the linear probing Wikipedia page make an assumption?
Here is the excerpt from the linear probing page at Wikipedia.
To search for a given key x, the cells of T are examined, beginning with the cell at index h(x) (where h is the hash function) and ...
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1answer
166 views
How to get all in constant time?
We are planning to design a system where following operations are supported.
...
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1answer
47 views
Efficient way to compute mod(w +1) or mod(w - 1) where w= 2^p
Knuth in his book provides a method of how to efficiently calculate mod(w +1) or mod(w-1) where w is a power of 2. I am not sure I could understand his assembly language completely.
Could you explain ...
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3answers
76 views
Is the capacity of a hash table a constant value?
In this paper, page 4, it is said:
"...there is always a constant expected number of elements that map to the same slot"
Assume we have a set $S$ of $n$ values, and we want to insert them into a ...
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1answer
84 views
Clarification reg. jump consistent hashing
I was reading the paper on Jump consistent hashing, and I'm having some trouble understanding one particular line (page 5, paragraph 2)
"Since we want P(j ≥ i) = (b+1) / i, we set P(j ≥ i) iff r ≤ (b+...
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1answer
139 views
Most space-efficient lossy dictionary?
Short version: What is the most space-efficient lossy dictionary (with given false positive and false negative rates)?
Long version: A lossy dictionary is a data structure $D$ that encodes a set $S$ ...
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87 views
Is this PJW hash function incorrect?
I came across this implementation of PJW and it seems incorrect:
...
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0answers
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Can I uses with same hashing-function for two hash-tables?
Given 2 hash tables , can I use only one hashing function for the two hash tables?
I don't sure if the size of the hash-tables is necessarily affect about the hashing-function that this hash-table ...
3
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1answer
43 views
Bounds on probe lengths and number of rehashes with universal hashing
Say I have a family of hash functions that are weakly universal, i.e. the probability of two non-identical keys $x\neq y$ are mapped to the same hash-value is bounded by $k/m$ when I have $m$ bins and ...
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0answers
68 views
Approximate dot product between neural network output layer's parameter vector and input activations with winner-take-all hashing
In the paper Deep Networks with Large Output Spaces, Vijayanarasimhan et al. describe their approach to approximating the dot product between a neural network's output layer's parameter vector and ...
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2answers
317 views
Perfect (or almost perfect) Hash function for n bit integers with exactly k bits set
I have a a data set with 2598960 elements of of unsigned integers of (at most) 52-bit length. The data set has a property that exactly 5 bits set.
This is only 1 data sets – I have similar data sets ...
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1answer
11 views
Method for eliminating spent hashes from a large collection?
Consider a DB with a large set of numbers, like hashcash tokens, where new numbers are constantly added(spent). Only numbers that has not been already added can be accepted.
Is there a functional way ...
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0answers
180 views
Proving a hash function family is weakly universal
$H$ is a family of weakly universal hash functions if for two elements $x,y$:
$$ P(h(x) = h(y)) \le \frac1m, $$
where $m$ is the size of the domain, and $h$ is chosen at random from $H$.
...
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1answer
50 views
Can anyone find a mapping from the set of all possible string to the natural numbers?
Can anyone find a map(injection) $h$ from the set of all possible strings $S^*$ to the natural numbers $\mathbb{N}$?
$$h : S^* \rightarrow \mathbb{N} $$
Assume $S$ is finite. I would prefer an ...
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1answer
25 views
Bloom Filter which does not fit in RAM [closed]
Is it possible to efficiently create a bloom filter with 10^12 buckets on a single machine with 32GB of RAM and a hard drive. We can assume that the keys are already on the disk and are small in size?
