Questions tagged [sets]
Questions about finite and infinite sets and multisets, related data structures and concepts.
366
questions
1
vote
1answer
24 views
set theory with RegEx on fen strings (or another parser)
how can you find if a regex call is a subset of another regex call on an predictable set of data
I have a string (chess Forsyth–Edwards Notation (FEN) string...
3
votes
1answer
49 views
A heuristic for finding the vector that is maximally distant from a set of vectors
I have two sets of vectors: A and B. I want to find the vector Bi in set ...
0
votes
0answers
16 views
Algorithm for bipartite graph matching decision problem
Suppose I have a list of sets
$$
L=\{A_1,A_2,\ldots ,A_n\}
$$
And want and algorithm that solves the following decision problem
Is it possible to select one element from each set such that no two ...
0
votes
1answer
25 views
Minimum spanning tree where weights of edges are intersecting sets
Given Graph $G=(V, E)$, where each edge in $E$ is assigned a "weight" as a set of elements. $w(e) = S_e \ \forall e \in E$.
Find a subset $E' \subset E$ such that it spans $G$, i.e., $E'$ ...
1
vote
2answers
53 views
What is the entropy of an unordered list?
I'm trying to compress unordered lists of a few thousand integers for transmission over HTTP, and Claude Shannon is disappointing me with his mathematical ambiguity :)
Each integer is 6-digits, so ...
2
votes
1answer
48 views
Is this a valid encoding of a tree structure using set theory and a valid way to extract the leaves from it?
I'm looking to formally define a tree and then extract the leaves from it in a concise way.
Does this look ok?
What is the best way of doing this?
$
Y = \{a,b,c,d,e,f,g\} \\
R = \{a \mapsto b, a \...
4
votes
0answers
74 views
Sequence where every subset exists as some contiguous subsequence
Given a set (i.e., a collection of distinct elements), how would you find a minimal sequence where every subset of that set can be found as the elements in some contiguous subsequences? The order of ...
1
vote
0answers
26 views
Selecting sets that maximise the cardinality of the union minus the cardinality of the difference
I have a sparse $60000\times10000$ matrix where each element is either a $1$ or $0$ as follows.
$$M=\begin{bmatrix}1 & 0 & 1 & \cdots & 1 \\1 & 1 & 0 & \cdots & 1 \\0 &...
13
votes
2answers
943 views
Recover a set with the information of the sums of all its subsets
I have a set $S$, which contains $n$ real numbers, which generically are all different. Now suppose I know all the sums of its subsets, can I recover the original set $S$?
I have $2^n $ data. This is ...
1
vote
0answers
29 views
Algorithm to find largest intersection of sets
This is a cross-posting from here, on the mathematics Stack Exchange. I thought this might be a more appropriate venue.
The problem is this:
I have a list of sets $$S_1, S_2,... S_N$$ where each set ...
0
votes
1answer
42 views
Is this way to combine two functions into a new function called a function product?
I have been looking for a maths operation that allows me to combine functions in a specific way. For example if we have functions f and g both with single mappings from o to e and v to c respectively, ...
1
vote
1answer
15 views
Complement of $\{w\#x \mid w,x \in \Sigma^*, T(M_w) \neq \{x\}\}$
This is one of my homework assignment questions, that are quite difficult for me.
The question states:
Show that $L$ is not semi-decidable where $L = \{w\#x \mid w,x \in \Sigma^*, T(M_w)\neq \{x\}\}$
...
4
votes
0answers
55 views
Combinatorics - how many $c$-distinct sets are possible?
I'm not sure if CS SE is the right place for this question, but since originally this question was in the CS area (and I translated it to a mathematical form), I will post it here.
I am given two ...
0
votes
1answer
16 views
Formal Description Of Data Structure For Infinite Sets Of Reals
The paper I'm working on uses sets as implemented in https://docs.sympy.org/latest/modules/sets.html. A set is stored in a data structure as a sequence of intervals with open or closed bounds, so it ...
1
vote
1answer
13 views
Set notation for ACL matrix
This might not be a computer science specific question and apologies if that is the case but it does come from material related to working out access control lists and I cannot understand the notation ...
1
vote
1answer
62 views
Find the element $x$ that maximizes $f(x)$ for $x \in \sum A_i$
I have a collection of sets $A_i \subset \mathbb{Z}$ where I want to find the global maximum after combining the sets using sumset.
The sumset is
$$ A + B = \{ a + b : a \in A , b \in B \} $$
and $R$ ...
2
votes
3answers
218 views
Set theory pertaining to category theory and functional programming
I'm reading an unfinished Introduction to Category Theory/Products and Coproducts of Sets and have come across the following:
A power set of a set is the set of all its subsets. A script 'P' is used ...
1
vote
0answers
19 views
Streaming maximum pair matching with limited memory
I am trying to find as many pairs of elements as possible from two distinct data streams, while being constrained by the number of elements I can hold in memory at any given time. Once a pair of ...
1
vote
2answers
25 views
Are joins/pullbacks of bloom filters possible?
An interesting advantage of bloom filters over hash tables, that they share with bitarrays, is that they support taking unions & intersections of sets by simply doing bitwise or & bitwise and ...
2
votes
1answer
52 views
What is the difference between Partition and Division?
While reading graph theory, I came across different definitions where they use partitions and divisions, I was wondering, are these terms same or different?
Can anyone explain me their difference in ...
2
votes
0answers
34 views
Online algorithm for compressing multiple SETS?
Algorithms like LZW and others compress data sequences.
What I'm looking is an algorithm that compress multiple Sets. if possible online algorithm.
For example :
...
1
vote
0answers
61 views
Disjoint groups using maximum matching
In the 3-Path Packing problem, we are given an undirected graph $G$ and a parameter
$k \in \mathbb{N} \cup \{0\}$. We need to answer Yes/No if there exists a collection of $k$ vertex disjoint paths on ...
1
vote
0answers
34 views
Minimal number of unions of sets such that no union has more than N elements
I have some sets, and can combine them by taking their union. I can take unions of the unions, too. I want to take unions until the total number of sets is as small as possible, with one caveat: that ...
0
votes
1answer
50 views
Tuple relational calculus: existential quantifiers
I have the following question and given answer:
Question: List the names of managers who have at least one dependant.
Answer: ...
6
votes
1answer
159 views
Shared Elements Algorithm
I have a problem that I am working on an algorithm for:
I have $k$ sets of distinct positive integers (each set is distinct, not necessarily across sets)
$S=\{A_1,A_2,A_3,...,A_k\}$ where $\forall A_i\...
0
votes
2answers
39 views
Is this the correct answer for the cardinality of this set?
This is a question from a practice quiz at my university.
Is the question asking for the cardinality of Σ1 = {a,b} to the power of four?
if that's the case, then the set would still have a ...
1
vote
1answer
22 views
Efficient cardinality of set overlap relation
Assume that we have a set S of sets s.
Every pair (s,s') in ...
1
vote
1answer
36 views
Families of sets indexed by another set
I am reading Automata and Computability by Dexter C. Kozen and I am in the first chapter entitled Strings and Sets.
If we have a set $A=\{ab,b\}$ do we get to assume that the null string $\epsilon$ is ...
3
votes
1answer
70 views
For two sets of points find if second one is result of linear transformation of the first
Say we have two sets of points in vector-2 space (In actuality need to solve this problem in vector-3 space but decided to start with a simpler problem). The points in the second set are the result of ...
0
votes
0answers
17 views
Given an abstract argumentation framework, is there a tool that can compute: conflict free, admissible and all extensions?
I am trying to find an online/offline tool that can compute the following:
Given an abstract argumentation framework <S, R>, where S = {a1, a2, a3, a4, a5} and the attack relation
R = {(a1, a2),(...
2
votes
2answers
92 views
Maximize number of subsets
Given a list of subsets $S_1, \ldots, S_n$ of the universal set $U = \{e_1,\ldots, e_m\}$, find a subset $S \subset U$ of size $k$ that contains the maximum number of subsets $S_i$. In another words,
$...
1
vote
1answer
25 views
Finding all subsets of a set of MultiSets made of elements from a single MultiSet (without replacement)
(originally asked on StackOverflow)
Two recent questions on StackOverflow by the same author1 are generally solved by the same technique. This feels to me like it would be a studied and perhaps well-...
1
vote
1answer
28 views
Find sets of weighted objects to maximize number of sets with weight >= X
I have N objects, each of which has a weight. I need to form combinations of the objects to maximize how many sets of objects add up to at least x total weight. Combinations can consist of any number ...
0
votes
1answer
38 views
How to implement conditional probability distribution on set-valued Random Variables
I'm trying to implement conditional probability distribution when the events of two RVs are sets. If I try to extrapolate concepts from real or categorical variables to sets things become confusing ...
1
vote
1answer
40 views
"The Annotated Turing" on listing all binary numbers between 0 and 1
In his book "The Annotated Turing" in the first sentence on page 32 Charles Petzold wrote:
These are binary numbers between 0 and 1, and (judging from the way we
created these numbers) all ...
0
votes
0answers
55 views
String membership in hash set time complexity
Given a string s and a hashset of strings words, what is the time complexity of the operation: ...
3
votes
0answers
27 views
Components of subset partial order
Given a collection C of sets, there are a number of proposed algorithms for building the subset partial order, e.g. this paper.
But is there any work on algorithms ...
3
votes
1answer
121 views
How to detect "tree-able" set-families?
A set-family (a set of sets of elements) is called tree-able if the elements can be arranged on a directed tree such that each element appears in exactly one node, and each set in the family ...
2
votes
1answer
62 views
Efficient Implementation of Boolean Lattice-Esque Operation
Let $X = \{1,2,\dots n\}$, and $Y_i= \{T \in \mathcal{P}(X): |T| \le i\}$. I am interested in "avoidance sets" $A \subset Y_n$. We say a subset $S \subset X$ is valid with respect to an ...
0
votes
1answer
64 views
Combinations of set unions
I have a set $S = \{0,1,2,3,4,5,6,7,8,9\}$. $S_i \subset S$ for $i = {1,2,3,4,5}$. Any three $S_i$ has the same union, that is $S_1
\cup S_2\cup S_3 = S_1\cup S_2\cup S_4 = ...=S_3\cup S_4\cup S_5 = A$...
6
votes
2answers
165 views
Spanning tree in a graph of intersecting sets
Consider $n$ sets, $X_i$, each having $n$ elements or fewer, drawn among a set of at most $m \gt n$ elements. In other words
$$\forall i \in [1 \ldots n],~|X_i| \le n~\wedge~\left|\bigcup_{i=1}^n X_i\...
2
votes
1answer
101 views
Find two disjoint set
Given an universum $U$ and two sets $A$ and $B$ of sets of elements from $U$. I want to find (if such a pair exists) $a \in A$ and $b \in B$: $a \cap b \equiv \emptyset$. Currently I can do it only in ...
2
votes
1answer
43 views
Optimal Selection of Non-Overlapping Jobs
I'm trying to find what the family of problem is - as well as an approach - for the following:
I have a set of tasks T = [t1, ..., tn] to do, each of which has a corresponding reward ri.
Each task ...
1
vote
0answers
50 views
Clustering sets by set difference
Suppose you have $n$ nonequal sets $S_1, \ldots, S_n$ and some constant $0 \le k < n$. The goal of set clustering is to find a partition of the set $\mathbf{S} = \{S_1, \ldots, S_n\}$ such that the ...
3
votes
1answer
624 views
C++ STL: How does the distance() method work for a set/ multiset (stored internally as a self balancing tree)?
I'm working on the problem: Count smaller elements on right side using Set in C++ STL
The solution is to add each element to the set and then to count the elements on the left, the distance function ...
1
vote
1answer
67 views
Algorithm to check Gibbs' Phase Rule
I am looking for an algorithm to solve the following problem. I am unsure whether to post this in computational science or here, but since this is an algorithm I thought I would try here first.
I have ...
1
vote
1answer
55 views
Need hint for bipartiteness proof
I am given a graph $G = (V, E)$ with $N$ connected components and $G^\prime = (V^\prime, E^\prime)$, where for each $v \in V$ there is $v_1, v_2 \in V^\prime$ and for each $(u, v) \in E$ there is $(...
0
votes
1answer
87 views
Splitting a group of numbers into $k$ sorted groups
I have this first task:
You have a set of numbers $S =\{ \dots \}$ of length $n$.
And a number $k$.
Both $n$ and $k$ are powers of $2$ and: $1 < k < n$
Your task is to write an algorithm (...
1
vote
1answer
100 views
Sets in Mathematics are immutable but in Computer Science sets are mutable and called "Dynamic Sets" - truth of the statement
While reading the classic text Introduction to Algorithms by Cormen et. al. I came across the following claim:
Sets are as fundamental to computer science as they are to mathematics. Whereas ...
1
vote
0answers
34 views
Set data structure for data too large to fit into memory
I'm trying to solve the following exercise:
Given N data items and memory that can hold M/B blocks of size B.
Describe a data structure that needs at most N/B blocks of external memory and allows ...
