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Questions tagged [sets]

Questions about finite and infinite sets and multisets, related data structures and concepts.

Sets have a long history in mathematics and its formalization. Various data structures exists for representing finite and infinite sets and multisets. Sets have close connections to the concept of a function.

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What exactly is the semantic difference between set and type?

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 differs from set theory, concretely. I understand…
user56834
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Boolean search explained

My mother is taking some online course in order to be a librarian of sorts, in this course they cover boolean searches, so they can search databases efficiently, however, she got a question sounding something like this: The search "x OR y" will…
sch
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Data Structure for Set Intersection?

Is there any data structure that maintain a collection of set (of finite ground set) supporting the following operations? Any sublinear running time will be appreciated? Init an empty set. Add an element to a set. Given two set, report whether they…
Dawei Huang
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in O(n) time: Find greatest element in set where comparison is not transitive

Title states the question. We have as inputs a list of elements, that we can compare (determine which is greatest). No element can be equal. Key points: Comparison is not transitive (think rock paper scissors): this can be true: A > B, B > C, C > A…
James Wierzba
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Problems for which algorithms based on partition refinement run faster than in loglinear time

Partition refinement is a technique in which you start with a finite set of objects and progressively split the set. Some problems, like DFA minimization, can be solved using partition refinement quite efficiently. I don't know of any other problems…
Juho
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What exactly is the semantic difference between category and set?

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 asking the same about categories: Every time I read…
user56834
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Given a set of sets, find the smallest set(s) containing at least one element from each set

Given a set $\mathbf{S}$ of sets, I’d like to find a set $M$ such that every set $S$ in $\mathbf{S}$ contains at least one element of $M$. I’d also like $M$ to contain as few elements as possible while still meeting this criterion, although there…
bdesham
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Computing set difference between two large sets

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 $A\setminus B$ and $B\setminus A$? In other words, how…
user917279
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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 far more than $n$, the number of unknowns.
S. Kohn
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What is complement of Context-free languages?

I need to know what class of CFL is closed under i.e. what set is complement of CFL. I know CFL is not closed under complement, and I know that P is closed under complement. Since CFL $\subsetneq$ P I can say that complement of CFL is included in…
user432
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How to find the maximal set of elements $S$ of an array such that every element in $S$ is greater than or equal to the cardinality of $S$?

I have an algorithmic problem. Given an array (or a set) $T$ of $n$ nonnegative integers. Find the maximal set $S$ of $T$ such that for all $a\in S$, $a\geqslant |S|$. For example: If $T$=[1, 3, 4, 1, 3, 6], then $S$ can be [3, 3, 6] or [3, 4, 6]…
drzbir
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Finding "fingerprint" sets

Let's say we have 10 people, each with a list of favorite books. For a given person X, I would like to find a special subset of X's books liked only by X, i.e. there is no other person that likes all of the books in X's special subset. I think of…
edron79
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Alternative to Bloom filter for extreme parameters

A Bloom filter is a space-efficient probabilistic data structure to perform membership-tests on a set (see Wikipedia's page for a definition; I use the same notations below). I am interested in a special application where the number of bits per…
doc
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What is a compact way to represent a partition of a set?

There exist efficient data structures for representing set partitions. These data structures have good time complexities for operations like Union and Find, but they are not particularly space-efficient. What is a space-efficient way to represent a…
cberzan
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Looking for a set implementation with small memory footprint

I am looking for implementation of the set data type. That is, we have to maintain a dynamic subset $S$ (of size $n$) from the universe $U = \{0, 1, 2, 3, \dots , u – 1\}$ of size $u$ with operations insert(x) (add an element x to $S$) and find(x)…
HEKTO
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