Questions tagged [graph-theory]
A field of combinatorics relating to the study of vertices and the edges that connect them
80
questions
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25 views
Formal specification (and algorithm) for coarsening of bipartite graph when nodes have identical connections
Apologies for lack of precise terminology. Not sure if this is a graph replications, coarsening, covering, or something totally different. The goal of this question is to (1) formally define this ...
2
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1answer
91 views
Bounds for the optimal bandwidth of 2D/3D FEM stiffness matrices
is anyone here aware of whether there exist bounds on the optimal bandwidths of 2D/3D FEM stiffness matrices?
Edit: more specifically, I would like to have bounds on the minimum bandwidth after ...
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1answer
715 views
How can I find the maximum equal-split flow of a network
I am working on a program currently that works out the maximum flow through a network using the Ford-Fulkerson algorithm, and that works fine, however, I need the final flow to meet the constraint ...
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0answers
76 views
How to distinguish primary hosts (stars) and orbiting satellites (planets) and tertiary bodies (moons) by their mass and trajectory?
I posted this question in the astronomy stackexchange. There are no responses, and it was suggested that I pose the question here. The "too long, didn't read" was taken from a comment, and ...
2
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0answers
62 views
Mesh partitioning with METIS
I am trying to use METIS-5.1.0 edition in order to partion a FE mesh. For demostration purposes I created 2x2 rectangle mesh and tried to partition it. However, I notice a weird behaviour in my code. ...
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1answer
26 views
Does computing all shortest paths in a simple graph result in a complete graph that follows a metric?
I have a simple graph $G=(V,E)$ that is not necessarily a complete graph. If I compute the shortest distance between every pair of vertices (let say with Floyd-Warshall algorithm) I get a complete ...
2
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1answer
116 views
Developing a meshfree contouring algorithm
I would like to find the contours of a scalar function $u(x,y)$ available as a discrete set of function values $u_i = u(x_i,y_i)$ over a scattered set of points $(x_i,y_i), i=1,...,N$.
In my case, the ...
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0answers
93 views
How to make a directed graph symmetric?
Say I have a directed graph given as an adjacency matrix $A$ in CSR format represented by the arrays ia (row indexes) and ja (...
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0answers
23 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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0answers
45 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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1answer
69 views
Newman algorithm yielding different result to what is given in his paper
Summary
I am trying to implement Newman's algorithm for community detection, outlined in this paper. I am testing my implementation against one of the datasets used in that paper to benchmark the ...
4
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1answer
235 views
Which optimization method can be used to do the following?
I've the following system of equations for studying information flow in the below graph,
$$ \frac{d \phi}{dt} = -M^TDM\phi + \text{noise effects} \hspace{1cm} (1)$$
Here, M is the incidence ...
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2answers
103 views
What is an instance (precisely) in computational complexity?
I am trying to understand the notion of reduction of a problem to another problem. As it is known this has huge impact on classifying the complexity of a problem.
The definition of reduction involves ...
1
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0answers
18 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 ...
2
votes
1answer
763 views
How can I determine if there is a closed-loop path in a graph?
Assuming I have a computer representation of a graph presented in the figure below:
How can I find out whether there are some close-loops inside the graph, like the one marked in red (or more ...
3
votes
2answers
152 views
Find shortest path around a cylinder represented by 3d triangular mesh
Suppose I have a 3d triangular mesh with the topology of a finite cylinder. Let $C$ be a vertex on that mesh.
How can I find the shortest path from $C$ to itself that goes around the cylinder? By ...
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0answers
24 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 ...
5
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2answers
345 views
Efficient algorithm to decide if a graph is a cactus?
A cactus is a connected graph in which every edge belongs to at most one simple cycle.
How should one modify the Depth First Search algorithm to obtain an efficient algorithm that determines if a ...
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1answer
259 views
Finding a shortest path in a graph
If each edge of a graph $G$ is unweighted or has equal weights, then the shortest path between two nodes in that graph is the path that contains the fewest number of edges. Such a path can be obtained ...
1
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1answer
56 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 ...
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1answer
1k views
How to reorder/cluster adjacency matrix to maximize the interaction along the super diagonal?
I have the following code which takes a DataFrame and plot the pdist matrix.
...
3
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0answers
184 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 ...
1
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1answer
180 views
Splittable and non-splittable flows in the network flow problem
I am working on a multi-commodity flow problem where for a graph $G=(V, E)$, some flows are permitted to be split and some flows should strictly follow one path. I have formulated this problem as ...
4
votes
2answers
430 views
Moore-Penrose pseudoinverse of singular rank degenerate matrix
I am trying to attain the Moore-Penrose pseudoinverse of a very large, very sparse, rank-degenerate, singular, and square matrix. ($75000 \times 75000$, near rank). The matrix is a graph Laplacian and ...
3
votes
1answer
159 views
Software for finding a minimum vertex cover for a hypergraph
A hypergraph $H = (V,E)$ consists of a finite set of vertices, say $V=\{1, \dots, n\}$ and a set of hyperedges $E \subseteq \mathcal{P}(V)$. We call $H$ a $k$-hypergraph if all $|e| = k$ for all $e\in ...
2
votes
2answers
376 views
Find connected circles
I have a problem as follows:
We have a set of circles (we know the radius r and the center point c in Rd of each circle)
We ...
0
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1answer
396 views
Hypergraph matching -> adjacency matrix?
I need to do a matching on a hypergraph. I read that in the case of a hypergraph there is no adjacency matrix.
How do I represent edges then?
0
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1answer
66 views
simple and fast graph-clustering for paralelization of finite element simulations
I'm learning to use OpenCL to optimize some of my simulations. I realized that I need some sort of Graph-clustering or graph-partitioning to exploit efficiently local memory for un-ordered meshes.
...
1
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0answers
348 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,...
4
votes
1answer
307 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
2k views
Can a Depth first traversal of a graph visit node more than once? [closed]
Is there a way in which Depth First Traversal will put a node into the stack more than once using the general algorithm as shown here.
Also, is it compulsory for all nodes to be entered into the ...
1
vote
1answer
79 views
Does the box-covering algorithm work also for directed graphs?
According to this article from Wikipedia, the box-covering algorithm calculates the fractal dimension of a graph. The algorithm is based on the concept of distance between nodes; see for example the ...
2
votes
2answers
639 views
PageRank using Inverse Iteration Method by Cleve Moler
I was trying to understand how to use the inverse interation method to compute the page rank as an exercise.
In this chapter (page 4) about page rank (by Cleve Moler), the author suggests to use the ...
1
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0answers
27 views
Chinese character component-based layout engine algorithms [closed]
I am looking for a PDF describing Chinese character component-based layout engine algorithms. These should allow for recursive encodings of radical and non-radical components, and the encodings should ...
1
vote
0answers
148 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.
...
13
votes
6answers
6k views
What is a common file/data format for a mesh (for FEM)?
I'm developing an FEM simulation. For early testing, I will use simple self-written mesher and visualisation of the mesh graph. But I want to prepare my program to use data generated by an existing ...
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0answers
49 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
vote
0answers
44 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?
5
votes
1answer
78 views
Optimal partitioning of a graph
Consider a planar graph, where each node is associated with a weight. I would like to partition the graph such that the sum of the node weights in each group satisfy a minimum requirement. However, I ...
3
votes
1answer
134 views
Sparse Matrix Reordering
Matrix reorderings are important for many direct solvers. Sometimes the objective is to reduce the bandwith or the generated fill in by LU Decomposition. I am interested in a reordering which reduces ...
5
votes
0answers
104 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 ...
5
votes
3answers
760 views
Minimization of non-linear function
Problem Summary
I am trying to estimate the (x,y) coordinates of each node in a graph, where I know the distances between connected nodes. For example
Given this ...
1
vote
1answer
191 views
Measure the differences in vertices density in a graph?
Lets say in Graph $G$ we have two vertices $v$ and $u$, each vertex is connected to several neighbors by edges describing the distances $d_{ij}$ from these neighbors. The neighbors themselves are also ...
3
votes
2answers
955 views
How to calculate efficiently mesh edges midpoints?
I have a 2D mesh of triangles used in Finite Element method to discretize the domain. I want to calculate the midpoints of all the edges because I want to use $\mathbb{P}^2$ elements. I am using ...
1
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1answer
90 views
Finding Common Side of Triangle
Given a triangulation (geometry), are there known algorithm in finding common side of triangles, that is O(N) or better?
0
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1answer
146 views
how to partition a graph(matrix) into subdomains with different sizes
i am studying the solver for PageRank problems which drived from the web link graph.
I have tried using METIS to divided the matrix into subdomains, but METIS can only produce subdomains with nearly ...
3
votes
0answers
73 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 ...
1
vote
1answer
818 views
Graph drawing with constraints
I have a (cyclic undirected) graph stored in a suitable structure (which depends on the language chosen). Nodes represent places in the real world and edges represent connection between them, so I ...
0
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2answers
415 views
How to represent molecules and compare equality
I originally asked this question at StackOverflow, and was suggested to bring it here.
I've seen this question about the representation of molecules in memory, and it makes sense to me (tl;dr ...
2
votes
1answer
95 views
graph theory operations to explore structure of a graph
I'm analyzing experimental data, and I've produced graphs that look similar to the attached sketch. When I look at the graph, I see structure in the connections (connections tend to be local, there is ...
