Questions tagged [graph-algorithms]
Algorithms on graphs, excluding heuristics.
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106 views
Star seperators to explain computational complexity of algorithms on a class of graphs?
A lot of NP-hard optimization problems on graphs which are perfect become solvable in polynomial time. Unfortunately, the class of graphs that arise in my problem are not perfect. The graphs can be ...
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113 views
Decomposition for a certain class of graphs
Suppose a graph, $G = (V,E)$ is characterized as a lattice/network of cliques as in the picture below. Does there exist some decomposition principle (i.e. on the right) for $G$, that yields some ...
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1answer
66 views
Algorithm for K-best NON perfect bipartite matchings
I was reading this great article: https://core.ac.uk/download/pdf/82129717.pdf
It solves a generalization of the maximum sum assignment problem by finding the k best assignments and not only the best....
6
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0answers
99 views
Grid-Minor Theorem of Robertson and Seymour and its Algorithmic Applications
Graph-Minor Theorem of Robertson and Seymour [1] states that if graph G has large treewidth, then it contains a large grid as minor. Most approximation results on general classes of graphs with ...
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84 views
Maximum Weight Independent Set on a Changing Graph?
Suppose I have an optimal solution to the maximum weight independent/stable set problem on an arbitrary graph. If I were to induce a clique among a subset of its vertices (and perhaps add in some ...
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0answers
37 views
Optimally fair stable matching
There's a nice post by Gil Kalai which outlines the inherent bias in stable matching algorithms quantitatively.
In the traditional loyd shapeley algorithm for $n$ men and $n$ women, given randomly ...
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1answer
71 views
When is extra vertex required in arbitrage detection using Bellman Ford?
I am studying applications of shortest path, in particular arbitrage.
Specifically, I was reading these two resources:
https://stackoverflow.com/questions/2282427/interesting-problem-currency-...
1
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1answer
74 views
Pulling a graph across a partition
I am looking for the name for a particular graph property, if it has been studied, and efficient algorithms for computing it, if they exist. I realise that this may be a well known property that I am ...
2
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0answers
116 views
Crime prevention using graph theory and machine learning
I am looking for a way to the model the incidence of crime among a network of individuals. Part of it will use machine learning, and part of it will have to resort to some graph theoretic ...
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28 views
Find a max flow in a flow network that passes through a fixed number of nodes
I want to solve a network flow problem with the usual setup of a directed graph with a capacity value for each edge. However, I also have an additional constraint: I want to find the maximum flow ...
1
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1answer
43 views
Problem property name where an optimal solution in a graph can be used as a solution in any subgraph
Suppose one is given a graph optimization problem where the optimal solution $S$ for the problem on graph $G$ can be used as a solution for any subgraph of $G$. In other words, given $S$ is an optimal ...
5
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1answer
106 views
Counting/Enumerating Minimal Edge Covers
A Minimal Edge Cover is an Edge Cover such that no other Edge Cover is a proper subset of it.
Questions
Which is the complexity of counting Minimal Edge Covers? Do we know any non-trivial ...
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44 views
Efficient topological sorting of the cartesian product of DAGs
Let us consider n directed acyclic graphs $(G_i)_{1\leq i \leq n}$ and G their cartesian product (with the induced edges) : G is still a DAG.
Let us suppose that each vertex has a value, defined as ...
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1answer
68 views
Color shifting in a bipartite graph
Assume that we have a directed bipartite graph $G = \langle L\dot\cup R, E\rangle $. Where $E$ contains directed edges only from $L$ to $R$, that is, $E\subseteq L\times R$. Assume further that the ...
2
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0answers
83 views
Counting the maximum number of paths of length $n$ that differ in at least $k$ edges
What is known about the complexity of solving (or approximately solving) the following problem?
INPUT: Graph $G=(V,E)$ and constants $L$ and $K$.
OUTPUT: The maximum size of any set $S$ of simple ...
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0answers
50 views
Reduction of irregular graphs, to regular graphs, while preserving hamiltonicity
I am wondering if this is a topic that has had research done...
If I could reduce irregular graphs to regular graphs (including replacing redundant node clusters with dummy nodes), while ensuring ...
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0answers
74 views
Partitioning directed graph
I'm a newbie in the mathematical field of graph theory (started to dive into it only few days ago) but I'm a very fast learner and have deep mathematical background. I'm trying to find/develop an ...
8
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1answer
183 views
Could chromatic number be easy to calculate when colouring is hard for some graph class?
Similar question was asked before, but there was an error in it so it was left unanswered Graph class with easy chromatic number, but NP-hard coloring
Is there any infinite set of graphs $C$ such as:
...
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37 views
Minimum cost circulation problem with bounded number of edges
Note: the question was taken from https://cs.stackexchange.com/questions/95479/minimum-cost-circulation-problem-with-bounded-number-of-edges
Since there was no answer in that forum (even after ...
2
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0answers
145 views
A variant of the Maximum Weight Clique problem
I am trying to solve a problem that I could reduce to the following:
Given a graph $G=(V,E)$ with both edge and vertex weights, all weights being non-negative, find a clique $Q\subseteq V$ s.t. $\sum_{...
3
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2answers
155 views
Finding a set which dominates the Minimum Dominating Set
Given an unweighted, undirected graph, a dominating set $S$ is a set of nodes such that every node is in $S$ or adjacent to a node in $S$.
The dominating set problem is NP-hard, but I am considering ...
4
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2answers
131 views
Max cut problem between two connected subgraphs
Let $G$ be a connected graph.
Consider the problem of finding a partition $G = A \cup B$ into connected subgraphs, so that the cut between $A$ and $B$ is maximized. Is there anything which is known ...
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1answer
98 views
Finding Cheapest n-Path [closed]
Given a weighted directed acyclic graph, how can I find the cheapest path from an Origin Vertex to a Destination Vertex which ...
2
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0answers
38 views
Min cut problem on unbalanced partitions for planar graphs with unit capacity edges
The question is: given a planar graph $G$ with unit capacity edge weights and a fixed positive integer $k$, what is an approximation algorithm for finding the minimum size of a cut $(A,B)$ with $|A|=k$...
5
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1answer
88 views
Exact algorithm or parameterized algorithm for Maximum Edge Biclique Problem?
The Maximum Edge Biclique(MEB) problem is to find a biclique with as many edges as possible in a bipartite graph. It was proved to be NP-complete by Peeters in 2003, and then the inapproximability ...
4
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1answer
141 views
Fast algorithm to find a maximum connected subgraph of k vertices
Given an undirected graph $G = (V, E)$ and a function $f: 2^V \to \mathbb{R}^+,$ where $2^V$ is the set of all subsets of $V$. Find a connected subgraph $T = (V_T, E_T)$ of k vertices such that $f(V_T)...
3
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1answer
108 views
Finding a “lowest” path in a graph
I have an undirected graph $G = (E,V)$, $|V|=n$,
where each node $v_i$ has a natural number weight.
Think of these weights as heights $h_i$.
Given two nodes $s$ and $t$, I'd like to find a lowest ...
4
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2answers
141 views
Check if graph stays connected after edge swap
Checking whether a (simple, undirected) graph is connected can be done in linear time in the number of edges. What I am looking for is a more efficient way of checking whether it stays connected after ...
3
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1answer
177 views
What exactly is Lawler's modification to Yen's algorithm and how does it work?
I recently read about Yen's algorithm, I understand the algorithm and it seems correct, however Wikipedia mentions that there exists "Lawler's modification" to the algorithm, which is described as ...
4
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1answer
323 views
Minimum Union-Sum Cost Path
I have a minimum cost path selection problem that is different from the usual shortest path in that each type of cost is accounted only once in the total cost of the path if multiple edges on the path ...
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0answers
53 views
k-center 2.0: A stronger k-center condition
Given an unweighted, undirected graph, we can use the classical 2-appx for $k$-center to select a set $S$ of centers such that every vertex is within a distance of 2 of some center in $S$.
Note that ...
3
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1answer
47 views
Complexity of distributively verifying that the diameter is small
Consider a graph $G=(V,E)$ and an integer parameter $k$.
I'm interested in the round complexity, in the CONGEST model, of checking if the diameter of the graph is "much larger" or "much smaller" than ...
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0answers
22 views
is there any result on mTSP over highly structured/modular graphs?
I am looking for theoretical results on mTSP (multiple travelling salesmen problem) over structured/modular graphs. If the meaning of "modular" is not clear, think about a graph that represents a ...
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0answers
24 views
explicit UES for $D$-regular graphs over $N$ vertices through the line graph
First of all observe that if we have $G$, a $D$-regular graph over $N$ vertices that is equipped with a consistent labeling $\ell$ then we can induce a consistent labeling for $L(G)$ the line graph of ...
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0answers
58 views
How to find cyclic ordering of edges incident on a vertex in a plane graph?
(I asked this on mathse. May be it suits better here)
How to find the cyclic ordering of edges incident on a vertex in a plane graph? (ie, in a plane embedding) Of coure we are looking for a ...
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1answer
224 views
Computing topological sort while keeping edges “short”
Motivation: I want to compute a topological sort order in which the connected vertices are close to each other.
Problem statement: Given a DAG $G(V,E)$ with $n$ vertices, compute a topological sort ...
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1answer
51 views
What is the deterministic complexity of counting the number of global minimum cuts on an unweighted undirected graph?
I know as a consequence of Karger's algorithm that the number of minimum cuts is bounded by $\binom{n}{2}$. In the comments of
Counting the number of distinct s-t cuts in a oriented graph
It says ...
6
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1answer
134 views
Partition edges into edge disjoint walks
Consider an undirected graph $G=(V,E)$ and two sequences of $k$ vertices $S=s_1,\ldots,s_k$ and $T=t_1,\ldots,t_k$.
A set of $k$ walks is called a $(S,T)$-walk partition if
the walks form a ...
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0answers
111 views
Is 3-coloring bounded degree graphs subexponential: $O(\exp{(\sqrt{n}\log^2{n})})$? [closed]
We got an argument that 3-coloring bounded degree graphs is subexponential
with complexity $O(\exp{(\sqrt{n}\log^2{n})})$.
The treewidth of a planar graphs on $n$ vertices is $O(\sqrt{n})$
and 3-...
5
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1answer
151 views
“Smallest” path that visits a given set of vertices
I use smallest rather than shortest to distinguish between the shortest path problem. The problem is as follows:
Given a directed graph $G=(V,E)$, two vertices $s$ and $t$, and a set of $p$ ...
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1answer
86 views
What is the best and easy (regarding implementation) way of computing three edge independent trees in a 3-connected graph?
I am searching for an implementation of an algorithm that constructs three edge independent spanning trees from a 3-edge connected graph. Any response will be appreciated. Thanks in Advance.
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2answers
368 views
Counterexample to max-flow algorithms with irrational weights?
It is known that Ford-Fulkerson or Edmonds-Karp with the fat pipe heuristic (two algorithms for max-flow) need not halt if some of the weights are irrational. In fact, they can even converge on the ...
13
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1answer
334 views
What are the obstructions to extending $L=SL$ to $L=NL$?
Omer Reingold's proof that $L=SL$ gives an algorithm for USTCON (In an Undirected graph with special vertices $s$ and $t$, are they Connected?) using only logspace. The basic idea is to build an ...
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0answers
66 views
Hypergraph Coloring Complexity
Dear can you help I am confused about the complexity of hypergraph coloring and finding the minimum number of colors
Finding the minimum number of colors for strongly coloring a k-uniform hypergraph ...
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2answers
179 views
Is perfect matching for bipartite graph with no cycles unique?
Given a balanced bipartite graph that satisfies Hall's theorem (is non singular) then it shown that it has at least one perfect matching.
My question is if the balanced bipartite graph is also ...
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1answer
231 views
Closeness Centrality for Weighted Graphs
In order to determine the Closeness Centrality for a vertex u in a graph, you compute the shortest path between u and all other vertices in the graph. The centrality is then given by:
$C(u) = \frac{1}...
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0answers
92 views
Path Finding: single-source, multi-path, multi-target, and max-depth - approaches and application
Background
Definitions (as used here):
$\qquad$single-source: for path finding, an algorithm is single-source if it searches from a given node.
$\qquad$multi-target: for path finding, an ...
6
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0answers
72 views
Complexity of bounded degree full contraction
This paper defines the problem $\mathrm{B{\scriptsize OUNDED} \ D{\scriptsize EGREE}\ C{\scriptsize ONTRACTION}}$ as follows:
Instance: A graph $G$ and two integers $d$ and $k$.
Question: Is there a ...
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0answers
82 views
Find the maximum induced (weighted) subgraph with edge weights greater than some minimum
I have a (fully connected) weighted undirected graph.
I want to find a maximal induced subgraph whose edge weights are all above some minimum value.
Or, if not a maximal subgraph, then with some ...
5
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0answers
165 views
Find a pair of nodes with maximum sum of distances in k given trees
For k edge-weighted trees $T_1,T_2...T_k$ which contain the same set of nodes $\{1,2,... n \}$, I want to find a pair of nodes $(x,y)$ which maxifies $$\sum_{i=1}^k d_i(x,y)$$ where $d_i(x,y)$ ...
