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Questions tagged [topology]

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Data Structures for Non-Orientable Manifolds

I am looking for a data structure to represent non-orientable manifolds (i.e. meshes like Moebius Strip, but without self-intersection). I will then implement other algorithms using this DS such as, ...
user63364's user avatar
7 votes
0 answers

Minimum Number of Edges Added to a DAG to get Unique Topological Order

The question is simple: Given an unweighted directed acyclic graph, $G = (V, E)$, what is the minimum number of directed edges we need to add to $E$ such that the resulting graph $G = (V, E')$ has ...
ryan's user avatar
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5 votes
0 answers

Elementary proof of compact space = exhaustible space?

The work of Martín Escardó has demonstrated close parallels between classical topology o one hand and computability on the other hand. (See for example "Infinite sets that admit fast exhaustive ...
Mark Dominus's user avatar
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3 votes
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How to get the minimal enclosed polyhedra in a Line framework (points connectivity lists)?

Greetings all and thank you. I'm a Ph.D. candidate working on a force structure's 3D tessellation project and get stuck. I've simplified the system into a set of lines linked together which formed a ...
Simon Shi's user avatar
3 votes
0 answers

Find internal surfaces in an oriented mesh

I have a solid with internal holes. My solid is mostly a union between walls/floors/ceilings. Each of them is a mesh with polygons oriented counter-clockwise. Then with those polygons I do a union ...
Marouane's user avatar
3 votes
0 answers

Scott/Lawson topology for function space domain

Given two domains, $D_1$, $D_2$, already equipped with Scott (or Lawson) topology, the product domain $D=D_1\times D_2$ has the Tychonoff product topology, e.g., Mathematical Theory of Domains, ...
John Forkosh's user avatar
2 votes
0 answers

What does point-free mean mathematically?

Point-free style is generally taken to mean a style of programming without explicit variables. I have some intuitions on point-free style but I want to know what the formal mathematical definition is. ...
Ms. Molly Stewart-Gallus's user avatar
2 votes
0 answers

Topology mapping (NoC)

My challenge is to derive three mapping scenarios separately for each memory module of the MPEG-4 to the 2-D mesh, so each task is mapped to a different core, and tasks are executed in parallel. Here ...
osobennyj's user avatar
2 votes
0 answers

In topological data analysis, do bar codes that begin and end at the same index mean anything?

The typical workflow in topological data analysis is from point cloud data to filtration to a list of bar codes corresponding to each dimension. A filtration is a sequence of simplicial complexes, ...
Eben Kadile's user avatar
1 vote
0 answers

ensure connectivity in geometric optimization

I am working on parts of my master-thesis and got to a problem which I would like to solve and develop some algorithm for. Basically I am dealing with 2d-geometry which I would like to represent using ...
Finn Eggers's user avatar
1 vote
0 answers

How to compute all inequivalent (under Aut(P)) nonnegative integer weight assignments (with fixed sum) to the vertices of a finite poset P?

Let $P$ be a poset on $n$ points, $\text{Aut}(P)$ its automorphism group, and $a_1,a_2,\dots,a_k$ the lengths of the orbits under $\text{Aut}(P)$. Goal: An algorithm to generate a member from each ...
mathematrucker's user avatar
1 vote
0 answers

Finding homotopies in a 2-complex

Are there any efficient algorithms to find the shortest homotopy between two paths in a $2$-complex?
Dan's user avatar
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0 votes
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Convert NURBS surface into Cubic Bezier Surface

The following post discussed how to convert(approximate) NURBS curve into cubic Bézier curve: Convert NURBS curve into Cubic Bezier Curve I am trying to come up with an algorithm that converts(...
John He's user avatar
0 votes
0 answers

Recovering graph given degrees and connectivity information

I have a graph and don't know how nodes in it are connected to each other. I know the number of nodes in the graph. I know the degree of each node in the graph. I know that given any node $A$ that ...
cs questions's user avatar
0 votes
0 answers

Classification of the Summit supercomputer

Can we classify a supercomputer in more than one group? For example, Flynn's classification, classification according to topology, classification according to memory access. For the Summit ...
A T K's user avatar
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0 votes
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How to cluster a dataset in which each data point is composed of a set of 2-dimensional coordinates

I have a dataset with totally $1000$ scenarios, each of which is composed of $5$ users' coordinates $(x_i,y_i), \forall i \in \{1,\dots,5\}$. Now, based on users' coordinates, I want to cluster these $...
Good to learn everything's user avatar
0 votes
0 answers

Machine Learning to draw a topology of elements

I'm exploring the idea of using machine learning to draw a topology of elements. For example, imagine a tree representing geological hierarchy (country -> province -> city). All countries are at ...
plsHelpMe's user avatar
-1 votes
1 answer

Sort sequence from topological sort if another value is being important

We have sequence that we got from topological sort, but because the graph may not be connected in all cases, we should sort this sequence with another factor. We should output permutation of numbers ...
someone12321's user avatar
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