**232 sets questions.**

Background
I have a list of 50 million $A-A_i$ pairs, where $i>1$, and $A$ and $A_i$ are some text. I need to extract the $A$ values from the list, so I get a new list of unique $A$ values.:
$$
\...

I have the following problem. The problem can be formulated in three different ways
Given sets $B_{-n},\ldots,B_n \subset \{1,\ldots,m\}$.
Find $i,j \in \{-n,\ldots,n\}$ with $|i| \neq |j|$ and $i,...

I have a set of (integer) ranges and want to compute the (possibly non-disjoint) set of all subsets of overlapping ranges. The data structure used for the output is not of particular importance to me; ...

Let there be a set of cardinality $n\in \mathbb{N}$. Let there also be $n$ subsets of that set. What is the smallest k such that union of some $n-k$ of those subsets is of cardinality at most $k$? The ...

Given a collection of sets $S_i$ of disjoint subsets $sub_i$ of a set $X$,
find a set $A$ of disjoint subsets $asub$ such that each one of these subsets is subset or equal to at most one subset in ...

I have been studying data structures. In that I have come across topics like Array being defined as Power set of cross product of set of objects and set of natural number and list being defined as ...

In this question, I asked what the difference is between set and type. These answers have been really clarifying (e.g. @AndrejBauer), so in my thirst for knowledge, I submit to the temptation of ...

Let $A\subseteq \{1\ldots n\}$ with $|A|=\alpha n, 0<\alpha\leq1$. Now we start generating random sets $B_i \subseteq \{1\ldots n\}$ with $|B_i|=\beta n$ where $0<\beta\leq\alpha$.
How many $...

Let $m, n \in \mathbb{N}$ and $n \le m$. Given $k$ subsets $X_1, X_2, \dots, X_k$ of $\{ 1, 2, \dots, m \}$ and $k$ nonnegative integers $a_1, a_2, \dots, a_k$, find all subsets $Y$ of $\{ 1, 2, \dots,...

I was digging through research articles to find a data structure that solves the dynamic sorted dictionary problem (representing any subset $S$ of a universe $U = \{0, \ldots, u\}$ with member/...

I am given an list of numbers and A number-s. I need to find out the collection(s) of numbers from the list of numbers whose sum corresponds to the given number s.
...

For homework I have the task
Assuming P ≠ NP, is the following set NP-complete:
{(G,w) | G is a Graph and w is a Hamilton cycle in G}
and I don't understand how to show that a set is NP-complete.
I ...

This question concerns the time complexity of outputting the unions of subsets of a given set.
Given $m$ subsets of an $k$-element set, can the union of those sets be computed in linear time with ...

I have the following problem:
Given a set a of n positive integers, write a backtracking C function that prints out all the subsets of a such that the product of their elements is p. Use an array ...

We have given a multiset of $N$ integer, both positive or negative. Consider all $2^N$ subsets, sorted by their sum (the empty subset has sum 0). We want an algorithm that outputs only the first $K$ ...

EDIT: I've now asked a similar question about the difference between categories and sets.
Every time I read about type theory (which admittedly is rather informal), I can't really understand how it ...

I'm interested to read about type theory, but I'm quite a beginner. I know what sets are and how to work with them, but I don't have a deep understanding of set theory. I don't really understand the ...

I am confronted with the following problem:
Let S be the family of all m-subsets of $[n] = [2m]$
let $S_1, S_2 \in S$ be distinct sets and let the state of storage be $State_1$ after stream $S_1$ is ...

The principle (called a Löwenheim–Skolem theorem by Huth and Ryan) states
Let $\phi$ be a sentence of predicate logic such that for any natural
number $n \geq 1$, there is a model of $\phi$ with ...

We can denote by $X\to X$ the set of all functions from $X$ to $X$.
Therefore, we can use the following statement to say that $f$ is a function from $X$ to $X$:
$$f\in X\to X$$
But we usually state ...

so for a homework assignment i need to prove the following:
We have arbitrary languages L1⊆∑1*, L2⊆∑2*, L3⊆∑3*, L4⊆∑4*Prove that the followging is either true or ...

I've been back and forth about this one. I have the following theoretical homework problem, which describes the SET-INTERSECTION problem. In my homework, it's ...

I have a large number of sets, A, B, C, ... where each set includes a few integers. I would like to find the set that includes the highest number of other sets.
A ...

This was an interview question that I was told is supposed to be an open ended discussion of the trade-offs.
You have a collection of comparable objects and want to be able to do the following:
1. ...

Can a Turing machine $M_A$ determine if the Turing machine $M_B$ accepts the set $W_k$?
I am curious about the answer to this as I am thinking about using the truth value of it on using it for a ...

Let's consider finite grid of points with size of $N$ by $M$ and set of $x$ points ($x$ is small number, up to 10, $N$ and $M$ are big numbers, up to 30000 )). Each of the $x$ points is described with ...

I have a collection of objects, with certain properties (let say 3 - zone, type, owner) only having a small predetermined possible set of values (like enum).
This is just a simple (javascript) array ...

I have a list of nodes l = [1, 2, 3, ... , n] and a list of tuples p = [(1, 2), (2, 3), ...], where the latter represents which ...

I'm reviewing my background in Algorithms and DS design. Specifically I never went through the van Emde Boas Tree. Though I can undestand the proto-vEB with related picture. I'm struggling to ...

Let $A$ denote a set that contains a relatively large number of different strings. Let $S_i$ denote these strings.
Let $B$ denote a set of sets such that each subset contains a (relatively small, ...

Given two sets of items
$A = { a_1, .., a_N }, B = { b_1, .., b_M },$
and assuming a connection weight $w{_i}_j \ge 0$ between any possible pair $(a_i, b_j)$ that contains one item of each set, how ...

In a partially ordered set L, an antichain is a subset A of L such that no two elements of A are comparable.
Antichains are commonly used to represent upward-closed subsets of L, that is, sets S such ...

I have two large sets of integers $A$ and $B$. Each set has about a million entries, and each entry is a positive integer that is at most 10 digits long.
What is the best algorithm to compute $A\...

Consider a sequence $s$ of $n$ integers (let's ignore the specifics of their representation and just suppose we have can read, write and compare them in O(1) time with arbitrary positions). What's ...

Is the intersection of infinitely many recursive sets $\bigcap_{i}U_{i}$ (where each set is different ) recursive? Recursively enumerable?
I know the union need not be recursive, because deciding if ...

I am trying to make sure my intuition for the following question from an assignment is correct
Prove or disrove: if $G = (V, E)$ is a graph and $I_1$ and $I_2$ are independent sets in $G$, then $I_1 \...

I am trying to think of how to optimize the following problem:
Let $S = \{1,2,...,N\}$. How many ways can $S$ be partitioned into non-empty subsets $P_1$ and $P_2$ such that $sum(P_1) = sum(P_2)$? I ...

I´m looking for an efficient algorithm that will find reverse cartesian products.
Mathematically, given $S \subseteq T^n$, I want to express $S$ as a union of sets $A_{i,1} \times A_{i,2} \times \...

I was trying to understand the definition of countable set (again!!!). Wikipedia has a very great explanation:
A set $S$ is countable if there exists an $\color{red}{\text{injective}}$ function $...

Given a set $S$ with a finite number of elements, where each $s_i\in S$ is itself a set with a finite number of elements, how do you partition $S$ using as few partitions as possible, such that all ...

I need to represent a family F of sets with some appropriate datastructure. The datastructure needs to support the procedures MAKE-SET(x), DISJOINT-UNION(A,B) and REPORT(A). I dont have a problem with ...

Let $S= \{1,2,3...,n\}$ be a set and I want to store a subset of $A \subseteq S$. Is there exists any data structure such that insert$(x)$, delete ($x$) can be done in amortised $O(1)$ time and search(...

I've got a set $Q$ of pairs $[S, v]$ where $S$ is a nonempty set and $v$ is a value ($v \in \mathbb{N}_{+}$). I need to find a subset $R$ of $Q$ with following properties:
Sum of all $v$'s is maximum
...

We have a finite poset and its subset $S$.
We can enumerate elements of $S$ using an iterator.
I need to check if there are more than one minimal elements of $S$ (regarding the above poset).
The ...

If I have a cuckoo filter containing {a,b} and another cuckoo filter containing {a,c}, can I union the filters to make one ...

I've written a political quiz based on data from the public whip. They group politicians' votes by policy; each vote can belong to many policies. There are too many policies for me to ask a question ...

Assume Alice and Bob have sets $A$ and $B$ of size $n$ each.
What are the most communication efficient algorithms for finding the intersection between the two sets if I know that the intersection is ...

Having trouble figuring this out.
If I have 2 sets of integers how would I use a hash table to test if set A is a subset of set B (in pseudocode).
I think I understand that basically I would need to ...

We are given $N$ sets of $M$ non-unique elements each.
The amount of overlap (computed as the element count in the set intersection) between the elements of these sets is stored in a $N \times N$ ...

I have two endpoints, $a$ and $b$, that can communicate through a channel. $a$ is storing a set of fixed-length strings $A = \{a_1, \ldots, a_{N_A}\}$, and $b$ is storing another set of fixed-length ...

- algorithms
- data-structures
- optimization
- combinatorics
- complexity-theory
- terminology
- formal-languages
- computability
- partitions
- graphs
- reference-request
- graph-theory
- algorithm-analysis
- np-complete
- trees
- finite-sets
- time-complexity
- regular-languages
- strings
- type-theory
- space-complexity
- discrete-mathematics
- coding-theory
- logic
- probability-theory

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