# 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 ...
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### 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 ...
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### 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 ...
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### 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 ...