Questions tagged [packing]

Packing problems are a class of optimization problems in which one has to pack objects together as densely as possible. One could be for example packing rectangles inside a rectangle.

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What's the complexity of solving a packing LP?

Linear Programming is in polynomial time weakly (when numbers are encoded in unary). AFAIK it remains open if it is possible to solve LP in polynomial time strongly (when numbers are encoded in ...
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Relations between the knapsack problem, the bin packing problem, and the set packing problem?

I wonder what relations are between the knapsack problem, the bin packing problem and the set packing problem? From their mathematical formulations, I don't see the first two belong to the third one ...
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Complexity of a non-linear knapsack problem

Minimize $$\sum_{i=1}^{n}\sum_{j=1}^{m_i}w_{i,j}v_{i,j}$$ subject to $$\sum_{i=1}^{n}\frac{m_i}{m_i+\sum_{j=1}^{m_i}v_{i,j}} < \theta$$ $$v_{i,j}\in\{0,1\}~\forall i,~j$$ where $w_{i,j}$ and ...
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60 views

Adversarial bin packing

An adversary gives you a set of items whose total size is $x$ (he gets to choose how $x$ is distributed. e.g. there may be $k-1$ items of size $\frac{x}{k}$ and 2 items of size $\frac{x}{2k}$). The ...
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Optimal distribution of N points in non euclidean volume, where each point is furthest away from the others

Given N points, I want to find the optimal configuration for which all the points are as far away from each other as possible. The metric I'm considering is an approximation to the perceived distance ...
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65 views

Hexagon packing algorithm

I'm trying to pack hexagons, within bigger hexagons, as shown here: For this example, I have 5 "children" to put in my "father" hexagon. Each time I've got too many children, I would like to reduce ...
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45 views

Packing the edges of a graph

Given a graph G, and positive integers k, q, pack the edges of G in (pairwise edge disjoint) connected sub-graphs, each of size (number of edges) at most k, and such that, no vertex is part of more ...
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108 views

Equally distributed/packed spheres within a sphere

I need to equally distribute a variable number of spheres within a larger sphere (the volume of the spheres depends on how many there are). Are there any algorithms for doing this? An approximate ...
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212 views

Job scheduling and packing algorithm

I was thinking about developing a daily production work plan algorithm for an enterprise. The problem is as following: There are various tasks that needs to be completed, each has a deadline, a ...
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107 views

Schedule repeating jobs of fixed length and different weights

I have a scheduling problem that I am not sure is a known variant with known algorithms. It does appear like bin packing problem at first, but after imposing the constraints, I am not sure what it ...
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55 views

A scheduling problem on an oriented graph with multiple constraints

The problem is the following : Data An oriented graph $(V, E)$ : to be understood as a set of partially ordered tasks A map $d: V -> \mathbb{N}$ : to be understood a function mapping tasks to a ...
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Multi Knapsack each with different constraints

It seems that there's no end to knapsack variations… here's the one I bumped into (at work): There are: N items, each with the usual value and weight properties. M bins, each with an upper ...
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For a given shape, find set of points with the maximum average distance

Within some shape, I want to find a set of points where the distance between each point is maximized. This seems similar to sphere packing to me except that part of the sphere can be outside the shape....