# Questions tagged [partitions]

A partition or partitioning of a set A is a collection of disjoint sets whose union yields A.

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### How to prove this “np-complete” problem?

I have a problem that I need to prove its np-completness: My original question I need to reduce it from some problem, i´m trying to do it from some other than knapsack, that´s why I ask again. I need ...
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### What is the trick of “adding a huge number” for in the reduction from 3-Partition?

Problem: To prove the $\textsf{NP-Completeness}$ of the problem of "Packing Squares (with different side length) into A Rectangle", $\textsf{3-Partition}$ is reduced to it, as shown in the following ...
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### Reducing partition to a partition where sum(partition1) = 3 times sum(partition2)

Given the following NP-complete problem: PARTITION Input: A list of positive integers $a_1, a_2, \dots, a_n$. Question: Can the list be partitioned into $2$ parts, $A_1$ and $A_2$, such ...
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### What exactly (and precisely) is “offset”?

Just like my previous question concerning 'hash'; what exactly is an (or the) "offset?" Is it a value or data type? Or is it an address location? I have heard it used in different contexts within the ...
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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 ...
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### 3-partition problem: why $b/4 < x_i < b/2$?

Why does the definition of the 3-partition problem contain the condition $$\frac{B}{4}<x_i<\frac{B}{2}?$$ I don't understand why leaving out this condition changes the 3-partition problem.
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### min cut for multiple partitions

So I am familiar with the standard minimum cut problem in which the goal is to find the smallest possible set of edges in a graph such that, upon their removal, we have two nonempty, disjoint ...
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### Reduction from 3-Partition to a cutting problem

My problem is the following: Input: a set of $m$ non-negative integers $\{b_1,...,b_m\}$ and a parameter $n$ with $n<m$. Output: $n$ sets of 3 numbers Task: Cut the $b_i$'s into $3n$ integers such ...
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### Partition partition with constraint of equal size

I see the problem here which is the well know partition problem but with constraint that the size of both sets must be equal. I look at the answer and I don't understand that why Colin said add max(S)...
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### Algorithm for random generation of two connected partitions of a finite set [closed]

Given the set $X=\{1,2,\ldots,n\}$; $\,\,$ $n=mp=kq$ where $m,k,p,q$ are positive integers. Please help me to programme an algorithm that realizes random generation of the following two partitions of ...
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### Finding all partitions of a set s.t. each block contains exactly one subset from a given set of subsets - how hopeless?

Hello and apologies if my question will be too elementary. My background is from arithmetic geometry, but I have been recently faced with certain computational problems of combinatorial nature, where ...
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### Reduction from PARTITION to MAX-CUT

I am trying to prove the NP-Hardness of the MAX-CUT problem. Other sources seem to reduce from the NAE-3SAT problem, however I have been trying to reduce from PARTITION because PARTITION and MAX-CUT ...