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Questions tagged [graph-theory]

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

1
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1answer
189 views

Efficiently generate a random subgraph (Gs) with maximum degree K, using only edges from an existing graph G

I am looking find a way of efficiently generating a random, undirected subgraph $G_s$ with $N$ vertices, using a subset of edges from an exisiting undirected graph $G$, also of size $N$, where the ...
0
votes
1answer
36 views

Vehicle Route assignment with capacity constraint

Problem Background I'm trying to find a solution/model to the following problem: Let's consider a cellular network (mobile network, ie., hexagonal cells) denoted $N$ composed of $|N|$ cells. Each ...
5
votes
0answers
2k views

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 ...
4
votes
0answers
75 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 ...
3
votes
0answers
98 views

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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0answers
66 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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0answers
128 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
85 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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0answers
171 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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0answers
116 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. ...
1
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0answers
42 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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0answers
39 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?