Questions tagged [packing]

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What is the complexity of pallet loading for identical non-rectangular objects?

In the pallet loading problem, we are asked to place a set of small identical 2-D rigid objects into a large bounding rectangle such that no two objects overlap. This problem is a special case of the ...
7
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676 views

Hardness of Approximation results for Special Set Packing Problem Wanted

Is there any inapproximability result for the following NP-hard problem, which is a special case of the weighted Set Packing Problem? The general Set Packing Problem would be: Given A Collection of ...
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208 views

What is the current "state-of-the-art" solver for quadratic knapsack problems?

New to this forum, so please let me know if my question format is incorrect. For linear KP with $n$ items and $c$ capacity, dynamic programming can find exact solutions in $\mathcal{O}(nc)$. I have ...
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106 views

Reduction from a geometric decision problem to its maximization problem

I am interested in the following NP-complete decision problem: ...
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264 views

Variation of bin packing

My problem is related to the standard bin packing problem, but in my case each item has a value, and the objective is to minimise the number of bins used to pack all the items PLUS the sum of the ...
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59 views

Bin packing where each item must occur in $k$ bins

I am looking for information on a generalization of bin-packing in which each item should appear in exactly $k$ different bins, for some positive integer $k$. The standard bin packing problem ...
2
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52 views

A "cut" packing problem

Consider the following maximisation problem. Given a path $P=\{1,2,\dots,n\}$ over $n$ vertices, a set $D\subseteq P\times P$ of "edges" and a set of positive integers capacities $\mathcal{C}=\{c_{i,...
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252 views

Can we find a generic tight example for the greedy algorithm of the unweighted generalized assignment problem?

In the unweighted generalized assignment problem (UGAP) we have $n$ items and $k$ knapsacks. For each item $i$ and knapsack $j$, there is a weight $w_{ij}$. Also, every knapsack has a capacity $W$. ...
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160 views

3D Bin Packing with one bin with infinite/unknown size

Hi I'm looking for a variation of the Orthogonal 3D-BinPacking algorithm with only one bin of unknown size. I have a set $S$ of $n$ cuboids items $i_j$ with $j=1...n$. The dimensions of the items are ...
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311 views

Bin packing upper bound: total size of items = k, bin size = r

Suppose you have items, whose total size (i.e. sum of sizes) is $k$. The number of items and their individual sizes are unknown integers. We need to pack the items into bins of size $r$. I need to ...
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45 views

Using bin-packing algorithms to approximate maximum-makespan

Bin-packing (BP) and maximum-makespan (MM) are dual problems. In both problems, the input can be defined as a set $S$ of positive integers, and the output is a partition of $S$. In BP, there is a ...
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34 views

Bin Packing And Preemptive Multi-Core Scheduling

I am trying to solve a preemptive multi-core scheduling problem, where the input is the tasks. The number of cores M can be decided after seeing the input tasks. I ...
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124 views

Maximize number of bins and minimize cost of elements chosen from a set

I am considering the following problem: there is a set of elements $S$ where each element is assigned to a bin $B$. The bins are disjoint and their union is $S$. There is also a cost function ...
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86 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 ...
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127 views

On algorithms that minimizes maximal load of bins

There are $n$ bins and $m$ balls, $b_i$ where $0<i\le m$. Balls are with different weights $w_i$ and have dependency between them. ball $b_1$ depends on $b_2$, $b_2$ depends on $b_3$, and so on. It ...