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Minimal/Small convex partition of a set of points
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Given a set of $n$ point tuples $(x_1, y_1), ldots, (x_n, y_n)$ with $x_i, y_i in mathbbR^m$. I am interested in a partition of a hypercube the points $x_1, ldots, x_n, y_1, ldots, y_n$ are contained in such that
- each element of the partition is convex, e.g., a convex polyhedron
- each element of the partition contains at least one $x_i$ or $y_i$
- if $x_i$ is contained in an element of the partition, $y_i$ must not be contained in it
Are there algorithms to compute or approximate a minimal partition? Can you point to existing implementations of these algorithms?
geometry discrete-mathematics graph-theory approximation convex-geometry
asked Jul 21 at 14:50
Markus
11
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up vote
0
down vote
favorite
Given a set of $n$ point tuples $(x_1, y_1), ldots, (x_n, y_n)$ with $x_i, y_i in mathbbR^m$. I am interested in a partition of a hypercube the points $x_1, ldots, x_n, y_1, ldots, y_n$ are contained in such that
- each element of the partition is convex, e.g., a convex polyhedron
- each element of the partition contains at least one $x_i$ or $y_i$
- if $x_i$ is contained in an element of the partition, $y_i$ must not be contained in it
Are there algorithms to compute or approximate a minimal partition? Can you point to existing implementations of these algorithms?
geometry discrete-mathematics graph-theory approximation convex-geometry
asked Jul 21 at 14:50
Markus
11
add a comment |Â
up vote
0
down vote
favorite
up vote
0
down vote
favorite
Given a set of $n$ point tuples $(x_1, y_1), ldots, (x_n, y_n)$ with $x_i, y_i in mathbbR^m$. I am interested in a partition of a hypercube the points $x_1, ldots, x_n, y_1, ldots, y_n$ are contained in such that
- each element of the partition is convex, e.g., a convex polyhedron
- each element of the partition contains at least one $x_i$ or $y_i$
- if $x_i$ is contained in an element of the partition, $y_i$ must not be contained in it
Are there algorithms to compute or approximate a minimal partition? Can you point to existing implementations of these algorithms?
geometry discrete-mathematics graph-theory approximation convex-geometry
asked Jul 21 at 14:50
Markus
11
Given a set of $n$ point tuples $(x_1, y_1), ldots, (x_n, y_n)$ with $x_i, y_i in mathbbR^m$. I am interested in a partition of a hypercube the points $x_1, ldots, x_n, y_1, ldots, y_n$ are contained in such that
- each element of the partition is convex, e.g., a convex polyhedron
- each element of the partition contains at least one $x_i$ or $y_i$
- if $x_i$ is contained in an element of the partition, $y_i$ must not be contained in it
Are there algorithms to compute or approximate a minimal partition? Can you point to existing implementations of these algorithms?
geometry discrete-mathematics graph-theory approximation convex-geometry
asked Jul 21 at 14:50
Markus
11
edited Jul 21 at 15:27
asked Jul 21 at 14:50
Markus
11
asked Jul 21 at 14:50
Markus
11
asked Jul 21 at 14:50
Markus
11
11
add a comment |Â
add a comment |Â
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