Questions tagged [space-partitioning]

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Arrange objects in space so that the outline takes the least surface/volume

Imagine you have a number of 2-dimensional objects. The question is how to fit them all in a rectangular space in such a way that this rectangle takes the smallest area possible. On the below image ...
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Data Structure for k Nearest Neighbour Search in D dimension using only point cloud as query points

I have a point cloud of N points in D-dimensional space with periodic boundary conditions, where N can range from 500 to 10^8 and D can range from 1 to 20. The distribution of points varies wildly, ...
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Sequential subsequence removal with arbitrary predicate

I want to extract sub-sequences from a sequence of float values. The "scale" and range of these values is arbitrary (as I can manipulate it at will) but the "shape" is consistent. For a visual ...
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Balanced $\epsilon$-separated partitioning by a hyperplane

Suppose we have $m$ points in $R^n$ and $\epsilon>0$ is a given constant. How can we find a hyperplane that the number of points that are $\epsilon$-close to it is minimum, with the constraint that ...
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balanced partitioning of nonconvex area between multiple agents in a grid world

In the original art gallery problem, there is a non-convex area provided and one has to divide it into regions based on infinite visibility of guards. We assume an unlimited number of guards. However, ...
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How to identify a continuous shape and break it into minimum number of rectangles?

The input in this case is going to be coordinates in 2D of the vertices of the shape. There will be no curves, but the shape can have holes. The algorithm or program needs to identify the continuous ...