Questions tagged [topology]

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5
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0answers
47 views

Analogue of the topology-computability correspondence for computational complexity

There is an interesting correspondence between notions of topology and notions of computability theory originating from the ingenious idea of Dana Scott to identify computable functions with ...
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2answers
68 views

Does DFS in an unweighted DAG find the shortest path for each vertex from a source?

I have many questions which related to this topic. I saw somewhere that a topological sorting can be used to find shortest path, and in DAG it can even find shortest weighted paths of all vertex by ...
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1answer
65 views

How to solve the minimum-cost flow problem on a complete graph, with a concave cost function of flow for each edge?

Here is the problem: Input: A series of source/sink nodes at fixed positions with given outwards/inwards flow Edges are NOT specified. The edges can connect any nodes. The total source and sink ...
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2answers
98 views

How to do a reverse topological sort using depth first search?

I'm doing a replacement for the venerable make utility that will support, among other things, automatic cleaning. The utility figures out automatically what files ...
5
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0answers
115 views

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 ...
5
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2answers
71 views

Topology vs sigma-algebra's as a framework for approximate information?

In the book "topology via logic" by Steven Vickers, topology is introduced for computer scientists, with the idea that topology captures the idea of approximate information. I am somewhat confused ...
2
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1answer
237 views

Convert NURBS curve into Cubic Bezier Curve

From this: Maybe you already know this, but it's impossible to convert nurbs to bezier splines exactly because nurbs are rational functions, and bezier splines are polynomials. I don't understand ...
2
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0answers
19 views

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, ...
-1
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1answer
90 views

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 ...
8
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0answers
92 views

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, ...
3
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0answers
98 views

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 ...
3
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2answers
596 views

Meaning of topological distance between 2 pixels

I came across the notion of topology and topological distance in the context of image processing several times (especially when it came to mathematical morphology). I looked for a not too abstract ...
3
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0answers
120 views

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, ...
8
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1answer
644 views

Is there a continuous hash?

Questions: Can there be a (cryptographically secure) hash that preserves the information topology of $\{0,1\}^{*}$? Can we add an efficiently computable closeness predicate which given $h_k(x)$ and $...
1
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1answer
152 views

Determining on whether topology is a tree or a hypercube

Assume that the nodes know that the topology G is either a hypercube or a tree. Assuming a unique initiator, design an algorithm to discover the topology. In other words, you would like a node to ...
2
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2answers
2k views

Divide self-intersecting polygon into simple polygons

My question is similar to question here Divide self-intersecting polygon I have points of self-intersecting polygon, its edges and also I am able to find points where it intersects. I have to divide ...
15
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1answer
756 views

Testing whether a tetrahedron lies inside a Polyhedron

I have a tetrahedron $t$ and a polyhedron $p$. $t$ is constrained such that it always shares all its vertices with $p$. I want to determine whether $t$ lies inside $p$. I would like to add one detail ...
5
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0answers
84 views

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 ...