Questions tagged [graphs]

For questions related to graphs, a mathematical object consisting of a set of nodes with edges connecting certain pairs of them.

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2
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1answer
75 views

Linearization of constraints in a ILP

I have been working on a Graph Theory problem for my thesis and got stuck about the linearization of some constraints. I am hiding everything, constraints, variables and so on, of my problem not ...
2
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1answer
89 views

Can't understand K-Truss Graph properties

Cross-posted on Mathematics SE. Since I have to implement an algorithm in the language of linear algebra, I'm trying to understand K-Truss Graphs which are defined as such The k-truss is a subset of ...
3
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0answers
43 views

Graph matching with apriori information about the matches?

Given two graphs with n vertices each, where apriori information regarding the similarity of each pair of vertices (between the source and target nodes) is given, is there a known concept for finding ...
5
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0answers
120 views

Reduction from Steiner Tree to TSP

The Steiner Tree version that I am considering is the following: given an undirected weighted graph $G=(V,E)$ and a subset of vertices $T \subseteq V$, find a minimum tree that connects all the ...
6
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2answers
201 views

Heuristic solution to the graph partitioning problem

I am working on a graph partitioning problem. A static column generation based solution was proposed in How to partition a graph with optimal number of groups? But I need some MILP solver to solve ...
5
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4answers
195 views

Numbering the vertices of an $n$-layer graph so that edges have similar numbered vertices on their ends

Consider a graph whose vertices can be partitioned into $n$ layers. Edges exist only between vertices in successive layers. So, there are edges between layers $1$ and $2$, between layers $2$ and $3$ ...
4
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0answers
193 views

Simplified risk game: writing a pratical Minimax objective for mixed integer programming

Problem To ensure fairness of the game, I am writing a bot that plays against itself. I have trouble rewriting a minimax objective to a practical maximization in mixed integer programming. The amount ...
4
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1answer
154 views

How to partition a graph with optimal number of groups?

I have a graph with $N=12$ nodes. Some nodes may not have any edge between them. every edge has a weight. How to find the optimal partitioning of the graph so that total weight in the system is ...
5
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1answer
129 views

Quickest shortest path algorithm

I want to do a shortest path algorithm. My direct and not acyclic graph contains only positive numbers. I have to do the scan for all pairs of nodes in complete depth in python. My graph is big (...
2
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2answers
81 views

Graph partitioning/cutting problem

Let $G = (V,E)$ be an undirected graph, with $e \in E$ has positive weight $w_e$. Given a set of integers $I = \{i_1,\dots,i_n\}$ such that $\sum_{k=1}^n i_k = |V|$. I want to find a partition $P$ of $...
4
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2answers
161 views

Any Solution for $k$-means with minimum and maximum cluster size constraint?

I am looking for an efficient approach to $k$-means clustering with minimum cluster size constraints. The clusters are non overlapping, so, one point can belong to only one cluster. $N$ be the number ...
5
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2answers
96 views

MAX-CUT: are there any algorithms or codes for classical computers, that cater to this specific case?

I missed the opportunity to ask this on OR.SE by 24 days! I asked it at CS.SE on 6 May 2019 and OR.SE entered Private Beta on 30 May 2019. It's a problem about minimizing a sum of terms that are ...
7
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2answers
417 views

Can a generic ILP solver find graph matchings as fast as a specialized algorithm?

Finding a maximum matching, or a maximum-weight matching, is a well-known problem, which has polynomial-time combinatorial algorithms. It can also be formulated as an integer linear program. In ...
1
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0answers
101 views

Simplex - Network flow problem : Arc from 1 to P with infinite capacity

The Network - Maximum flow problem below aims to find the maximum flow using simplex method : With the LP as follow : LP : \begin{Bmatrix} Z(Max) = \sum_{i=1}^{m} fi \\ Af =0 \end{Bmatrix} ...
3
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2answers
79 views

IP model for k-rooted spanning forest

I am looking for an IP model for finding a $k$-rooted minimum spanning forest on an undirected graph $G$. Given a set of roots $R$ and a set of nodes $N$ $(R\cap N=\emptyset)$, I would find a forest ...
1
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1answer
64 views

Minimum vertex cover and linear programming 2

This is a modified version of the algorithm that I have proposed here. Suppose we have a graph G. Consider the minimum vertex cover problem of G formulated as a linear programming problem, that is for ...
3
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0answers
38 views

Power grid distribution and recipient bias

I have a strong feeling that this problem I'm trying to solve has already been done by someone much smarter than me at one point and I'm more looking at where I can research a topic further rather ...
1
vote
1answer
81 views

Find minimum cost problem

The problem below aims to find the minimum cost for the network architecture: We want to build a network where client terminals are connected to servers by cabling which is very expensive. The network ...
4
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1answer
74 views

Does anybody know the complexity of finding a maximum clique in circulant graphs?

I would be interested in knowing if finding a maximum clique in circulant graphs is NP-hard? Does anybody have any pointers or papers to suggest?
1
vote
1answer
61 views

Handy way to index set of tuples in AMPL

I am dealing with a discrete math optimization problem on a complete graph. My variables are the arcs but I want to delete the arcs that "cost too much". I have $n$ nodes which means I have $...
1
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0answers
26 views

Create randomly an undirected connected graph using Matlab [closed]

I want to create randomly an undirected connected graph $G=(V,E)$ with $n$ nodes and $m$ edges using Matlab. How can I do this?
9
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2answers
420 views

How to maximize "contrast" between nodes on a graph?

I have an undirected graph such as the one shown below. I can make up to 3 choices about the color of each node. The edge weights are equal to the difference between the nodes, given by the "...
0
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1answer
134 views

Miller-Tucker-Zemlin subtour elimination constraints to obtain a minimum spanning tree

I need Miller-Tucker-Zemlin subtour elimination formulation for symmetric traveling salesman problem (STSP) to use to construct a minimum spanning tree. Ie, I need Miller-Tucker-Zemlin formulation ...
7
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1answer
472 views

Minimum vertex cover and linear programming

Suppose we have a graph G. Consider the minimum vertex cover problem of G formulated as a linear programming problem, that is for each vertex $v_{i}$ we have the variable $x_{i}$, for each edge $v_{i}...
2
votes
1answer
216 views

Ordering Nodes of a graph according to their degree

In an undirected graph, I would like to order its nodes according to their degree. However, to do this I have to enter the edges of the graph first. When I do this, NetworkX in Python reads the nodes ...
2
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0answers
70 views

Node ordering in Graph optimization

I'm solving a network optimization problem which is modeled as a graph $G=(V,E)$. Solving this problem using Pulp and NetworkX in Python and ordering the graph's nodes in a certain order (i.e. (1,2,3,...
5
votes
2answers
250 views

Shortest path problem with underlying continuous variables

I recently got interested in the following variation of the shortest path problem. I've looked in the literature for days but I couldn't find any paper studying this problem. I'd like to ask if you ...
3
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0answers
59 views

Simplex method on graphs: How do I find a basic solution using the Ford-Fulkerson algorithm?

I'm tasked with solving a minimal cost flow problem. I'm asked to first use the Ford-Fulkerson algorithm on my graph to find a basic solution that will then be used to do the simplex method on that ...
2
votes
1answer
65 views

Algorithm / Method for determining N nodes to disconnect group of nodes

Hell everyone I have been trying to read through this forum for the methodology to approach a graph/network problem. The idea is I have an undirected graph, and every node is capable of talking to any ...
6
votes
1answer
194 views

What is intended when we use "robustness", "resilience" and "reliability" in Operations Research?

I will use an example to detail my question but I would like you to keep in mind that I wanted to define: Robustness, Resillience, Reliability in the most general case within Operations Research. ...
6
votes
3answers
291 views

How to find all descendant vertices of all vertices in a big DAG (Directed acyclic graph)?

A simple algorithm may be traverse all vertices, and perform DFS for every vertex. However, the computational complexity is $O(n(n+m))$, where $n$ and $m$ are the number of vertices and edges in the ...
4
votes
1answer
59 views

What is the name of the graph where any edge is part of a cycle?

I wonder if there is a special category for this kind of graphs, I am thinking of a bidirectional graph but it would also be interesting in the cases when it is undirected. I am thinking of something ...
2
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0answers
45 views

Is this a common generalization of the independent set problem?

Suppose a minimum weighted independent set in a conflict graph with $n$ vertices. The basic version is where each vertex $i$ is associated with a weight $c_i$. i.e., there is a vector $C$ for the ...
3
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1answer
255 views

social network analysis - relations between people with weights

I asked this question on datascience.stackexchange but they directed me here. I have a social network represented as a set of people $S$ and individual weights for each of person (weight is the cost ...
4
votes
1answer
103 views

Clustering a large ride-matching problem

Background: We are solving a large scale vehicle to person ride-matching problem. The problem is essentially simple (match every person with a vehicle, if possible), yet the problem size is quite ...
8
votes
1answer
64 views

Covering problem on a network (?)

I have this problem described in natural language, and I was wondering whether it is relatable to any known problem. I have a directed acyclic graph. Each node can host a "probe". If node $i$ hosts ...
4
votes
2answers
142 views

Maximum Flow Problem : Can someone refer me to accessible valuable resources

Can anyone please refer/suggest me some accessible papers, works, books, websites, documentation related to The Maximum Flow Problem.
7
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1answer
1k views

How to use the least number of colours to colour different routes of a bus route such that no two intersecting routes will have the same colour

I would like to know of a method in which if provided say 10 routes with details regarding which route intersects with which another route, we can use the least number of colours to colour the routes, ...
3
votes
2answers
161 views

Could DOcplex.CP recognize that it solves the graph coloring minimization problem?

I created a graph coloring DOcplex.CP model inspired by this example. However, I do not know the number of colors in advance. The goal is to minimize the number of colors (i.e., get as close as ...
6
votes
1answer
79 views

Maximum weight b-matching with global cardinality constraint

Suppose $A$ is an $n$-by-$n$ symmetric matrix whose entries are all nonnegative. $A_{ii} = 0$ for all $i$. We want to find an $n$-by-$n$ binary ($0/1$ valued) matrix $X$ that maximizes $$\sum_{ij} A_{...
16
votes
1answer
227 views

Was there something specific that caused graph cuts to lose popularity in the last 5 years?

Almost every graph-cut paper I look at seems to have exactly the same pattern of monotonic growth in citations and then monotonic decline starting around 5 years ago: For privacy I've cut the all ...
7
votes
2answers
534 views

The general meaning of "constraint relaxation" in the context of the Shortest Path Problem

I've read that in the context of the Shortest Path Problem, the use of the term "relaxation" ("relaxing edges") [...][the use of the term "relaxation"] is historical. The outcome of a relaxation ...
12
votes
1answer
135 views

Re-calculating shortest path in slightly altered graph

I was wondering if someone has come across this before and/or has a smart idea for the following: I have a directed graph $G$ with costs $c$ associated with the arcs, and I know the shortest path $P^...
8
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0answers
74 views

Multiple shipments with FILO order

I am trying to solve a problem statement with the help of jsprit. There is a depot. Identical items need to be delivered or picked up. An item can have two states: Bad or good. Bad items need to be ...
24
votes
4answers
719 views

What are the tradeoffs between "exact" and Reinforcement Learning methods for solving optimization problems

Exact methods, e.g., models that utilize an MIP approach with a specified objective and constraints, have advantages like the following: Using off the shelf solvers Optimality gap provability ...
6
votes
1answer
354 views

Network flow model - How can I turn this diagram into a matrix that when converted to RREF solves for max flow?

I have the following network flow model diagram and I have already calculated maximum flow using the R package igraph to be 28. However, what I would like to know ...
9
votes
1answer
620 views

A variant of the Shortest Path Problem

Consider a layerwise directed acyclic graph DAG, $G=(V,E)$ and two vertices $s$ and $t$. $s$ is connected to all vertices in $L_0$, $L_0$ is connected to all vertices in $L_1$ and so forth. Consider ...
14
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3answers
2k views

A variant of the Multiple Traveling Salesman Problem

I am trying to find a reference (or a reformulation) of a variant of the multiple Traveling Salesman Problem, where multiple agents need to visit each vertex in a graph with minimal cost. Most of the ...
7
votes
1answer
115 views

References for "metric" network flow problems

Network flow problems are very well studied in the literature (e.g., see the Network Flows book), and the first DIMACS challenge was dedicated to these problems. Very efficient implementation of ...
13
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5answers
261 views

Connectivity of two nodes in an arbitrary undirected graph

Is there an efficient way to model the connectivity of two nodes in an arbitrary undirected graph? I would like to have a binary variable representing this connectivity: 1 if there exists a path ...