Questions tagged [graph-theory]

A field of combinatorics relating to the study of vertices and the edges that connect them

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Two-chordless cycle extraction from a failed comparability graph recognition

I have implemented a comparability graph recognition algorithm from M.C. Golumbic's "Algorithmic graph theory and perfect graphs" book. It is hinted in Fekete, Schepers, and van der Veen's "Exact ...
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88 views

Graph optimization for parallel processing

Consider the following example structure of overlapping images marked A,B,C,D. The possible overlaps are marked by gray color: The structure can be represented by a weighted undirected graph (images ...
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Factorize laplacian in terms of first derivative matrix

I am trying to factorize the following Laplacian matrix in terms of $ D^TD$, D is the first derivative matrix. The tridiagonal form of the secon derivative matrix using Neumann boundary condition is ...
3
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68 views

Absorbing BC's / PML on a graph

The wave equation, $$\ddot{u} = c^2 \Delta u,$$ can be generalized to abstract graphs by using the negative graph Laplacian in place of the physical Laplacian. Is there a graph-theoretic analog of ...
3
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131 views

The traveling salesman problem - Using Space Renormalization

Image attached is where I am at the moment. Blue dots=points/cities, Black x's represent central points in each box that contains at least one city, and pink dots represent the midpoint of these ...
2
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0answers
97 views

Algorithm for optimizing graph interconnectivity

I have a partiuclar kind of graph problem and (not having a background in graph algorithms) I would like to know how this kind of problem is called in the literature and what algorithms exist for ...
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40 views

Is there some algorithm to find the shortest path in the context of genetics and breeding?

In genetics and breeding, we typically have two parent genotype (may or may not be the same) which can produce a set of offspring with certain probability (assuming simple Mendelian inheritance). I ...
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13 views

polylog implementation of fully-dynamic graph connected-components?

I have read about papers in the last 20 years that have solved this problem. Many are mentioned in http://jamiemorgenstern.com/teaching/s18-6550/notes/notes-lec4-dgc.pdf Unfortunately the only ...
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18 views

Find all recurring subgraphs/patterns of maximal size in a single undirected, labeled, connected graph

I would like to identify all subgraphs of maximal size (maximum number of nodes) that are recurrent in a single undirected, labeled, connected graph. I provide exemples of input and expected output ...
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239 views

First approximation to the TSP in a non-complete Graph

I'm trying to solve the Travelling Salesman Problem in a non-complete graph $(G,E)$ using genetic algorithms. My problem is that I can't find a good first approximation by the usual greedy algorithms,...
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128 views

Updating factorization of Laplacian (add/remove edges)

For a graph $G=(V,E)$, recall that the unweighted Laplacian is $L:=D^\top D$, where $D\in\{-1,0,1\}^{|E|\times|V|}$ is the graph "gradient" operator that subtracts adjacent vertex values onto edges. ...
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45 views

Alternative to two “for” loops in finding best neighborhoods for TSP?

I am trying to solve Travelling Salesman Problems using tabu search. I have been able to successfully find "near enough" optimal solutions (as well as one optimal, yay!). For the moment I am using ...
1
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41 views

Interior nodes of a closed graph?

Does anybody know if any graph partitioner library such as Metis, Scotch, or Zoltan can (besides splitting a domain), differentiate between internal (i) and boundary (b) nodes?
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18 views

Benchmark instances for directed 3-Cycle cover

The directed 3-Cycle cover asks for a vertex-covering set of oriented cycles with at least three vertices per cycle such that every vertex is covered by exactly one cycle. I have scrutinzed the ...
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23 views

Controllability - Maximum Matching

I found this image on wikipedia referring to Barabasi's work on Network Controllability. I tried to verify it. We have a A matrix of dimensions (20 by 20) made as the image suggests. According to the '...