Stack Exchange Network

Stack Exchange network consists of 174 Q&A communities including Stack Overflow, the largest, most trusted online community for developers to learn, share their knowledge, and build their careers.

Visit Stack Exchange

Questions tagged [graph-algorithms]

Algorithms on graphs, excluding heuristics.

0
votes
0answers
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 ...
0
votes
0answers
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 ...
1
vote
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
votes
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 ...
0
votes
0answers
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 ...
1
vote
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 ...
-1
votes
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
vote
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
votes
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 ...
0
votes
0answers
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
vote
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
votes
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 ...
0
votes
0answers
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 ...
1
vote
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
votes
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 ...
1
vote
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 ...
0
votes
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
votes
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: ...
0
votes
0answers
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
votes
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
votes
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
votes
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 ...
-2
votes
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
votes
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
votes
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
votes
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
votes
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
votes
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
votes
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
votes
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 ...
1
vote
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
votes
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 ...
0
votes
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 ...
0
votes
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 ...
0
votes
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 ...
6
votes
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 ...
0
votes
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
votes
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 ...
3
votes
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
votes
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 $p$ ...
1
vote
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.
8
votes
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
votes
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 ...
0
votes
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 ...
1
vote
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 ...
-1
votes
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}...
0
votes
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
votes
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 ...
0
votes
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
votes
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 $d_i(x,y)$ ...