Questions tagged [partition-problem]

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FPTAS for Number Partition Problem

I've been given a task to implement two algorithms (an exact algorithm and fully polynomial approximation scheme) for number partitioning problem. I found out that I can use some modification of ...
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1answer
209 views

Expansion vs Sparsest cut

let $G=(V,E)$ and $S\subsetneq V$ then expansion of set $S$ is $$\alpha(S)=\frac{|E(S,\overline{S})|}{\min\{|S|,|\overline{S}|)\}}$$ where $\bar{S}=V\setminus{S}$ and $E(S,\bar{S})$ are edges ...
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1answer
101 views

partition to min the max number of intersections

Given $n$ items and $m$ customers, each of whom is interested in some subset of the items, partition the set of items among $k$ different stores so that the maximum number of customers visiting any ...
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0answers
659 views

Approximation results for 3-partition

The 3-partition as defined here is a strongly NP-complete decision problem. Consider one optimization problem of 3-partition where the $m$ subsets each have at most three elements and a sum of not ...
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1answer
1k views

Graph building with weighted nodes

I have a set of nodes which can be connected together through arcs. Every node has an associated value, reflecting the "fitness" that this particular node has in the graph. I have to find the best ...
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0answers
81 views

Partitioning based on distribution

Having a set of numbers $S={s_i}$, I want to assign them to bins, $b_i$, such that the sum of items on bins follow a specific distribution. For two bins and uniform distribution, this problem is ...
4
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1answer
189 views

Set partitioning algorithm

I'm a working software engineer and I'm trying to develop some planning software. I have faced the following problem. I have some finite set $ U $ of some distinct elements $ e_i \in U $. I have ...
8
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0answers
749 views

Is this minimization problem NP-Complete?

We are given an $n \times (n + k)$ matrix $A$, with entries in GF(2), of the form $A =[I_n\ B]$, where $I_n$ is the $n \times n$ identity matrix, and $B$ has no "zero" rows or columns. The problem is ...

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