Questions tagged [sets]

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

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Set Intersection with asymmetric set sizes

I'm looking for an algorithm to perform set intersection where set $N_1$ is very small and set $N_2$ is very large. Due to the constraints of the problem I am solving, I cannot rely on an algorithm ...
61 views

Language intersections (set theory) - Understanding better

I've joined computer science classes at high school because I have a wide knowledge and a few years of experience in programming in multiple of languages, however I didn't fit in the requirements of ...
578 views

Finding set of disjoint sets with additional value optimization

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 ...
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How to apply “verification” and “decision” for the SUBSET SUM problem?

The SUBSET SUM problem states that: Given finite set S of integers, is there a subset whose sum is exactly t? Can someone show me why verification is simpler ...
1k views

Minimize sum of squared error

I have an array of real numbers, I want to partition them into k sets. In each set, I calculate the sum of squared error. Then, I add up all the sum of squared error for all the set. I want to ...
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Reconstruct directed graph from list of ancestors for each node

I have a problem that I encountered that boils down to the following: Considered this directed graph I found on Google: I have the following information available to me ...
63 views

What is the name two mutually idempotent functions?

To clarify, in haskell, there is an ord function that gives the byte integer of a character (i.e. ord 'a' yields ...
320 views

Asymptotic lower bound on the number of comparisons needed to find the intersection of unsorted arrays

A homework problem in my current CS class asks us to produce a comparison-based procedure for taking (essentially—there are some poorly-specified rules about duplicates) the set intersection of $k$ ...
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Total ordering of sets of fixed size

I'm curious if there is a name for this way of ordering finite sets of natural numbers (shown here for the case 3 elements, but can be extended to any number of them): ...
1k views

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 ...
444 views

Most common subset of size $k$

I'm trying to write an algorithm that detects the most common subset of at least size $k$, from a collection of sets. If there are ties for the most common subset, I want the one of them whose size ...
112 views

Number of K-sets [closed]

I am having a plane in N dimension. Th distance between 2 points (a1,a2,...,aN) and (b1,b2,...,bN) is max{|a1-b1|, |a2-b2|, ..., |aN-bN|}. I need to to know how many K-sets exist(here K-set refers to ...
184 views

Set packing variant

There are n collections of M sets. Pick a single set from each collection, such that all n picked sets are pairwise disjoint. This problem can be converted to the ...
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Equivalence of independent set and set packing

According to Wikipedia, the Independent Set problem is a special case of the Set Packing problem. But, it seems to me that these problems are equivalent. The Independent Set search problem is: given ...
823 views

Finding number of maximum independent sets in tree, using dynamic programming

I'm quite stuck trying to answer this. The problem of finding the size of the maximum independent set in a tree using dynamic programming is well documented and many solutions are around. I've been ...
449 views

Is the set-partition problem polynomial time reducible to the subset-sum problem?

There are many solutions on the web showing that the subset-sum problem is polynomial time reducible to the set-partition problem. However, during my search, I came across the following powerpoint ...
Here is a definition from the functions section in my discrete math textbook (Discrete Mathematics and its Applications 7e, Rosen 2012): Let $f$ be a function from $A$ to $B$, and let $S$ be a ...