Questions about graphs in which every edge is associated with a weight.

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1answer
49 views

Shortest directed path connecting given subset of vertices

Given weighted directed graph $G = (V,E,w)$, where $w : E \to \mathbb R^+$ source vertex $v \in V$ vertex subset $U \subset V$ how to find a shortest directed path from $v$ containing all vertices ...
1
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0answers
80 views

Algorithm to determine a minimal cost graph [closed]

I'm trying to solve this problem: Given a collection of cities and the number of commuters between cities, design a network of roads for minimal cost where cost includes the cost of building the ...
12
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1answer
281 views

Why does Dijkstra's algorithm fail on a negative weighted graphs?

I know this is probably very basic, I just can't wrap my head around it. We recently studied about Dijkstra's algorithm for finding the shortest path between two vertices on a weighted graph. My ...
1
vote
2answers
210 views

Dijkstra's algorithm for edge weights in range 0, …, W

Suppose I want to run Dijkstra's algorithm on a graph whose edge weights are integers in the range 0, ..., W, where W is a relatively small number. How can I modify that algorithm so that it takes ...
-1
votes
1answer
231 views

Calculating the number of non-intersecting routes in an Euclidean graph

I have an Euclidean graph: each vertex is a point on the 2D plane, so the weight of each edge is the Euclidean distance between the vertices. I found a geometric proof that every optimal TSP solution ...
2
votes
0answers
46 views

Is there a relationship between graph entropy and node entropy?

Eagle, et al [1] discuss the notion of node entropy and this is captured in igraph via the diversity metric. I was wondering if there was any relationship between these node entropies and the idea of ...
-1
votes
1answer
113 views

Efficient way to find intersections

I have an Euclidean graph: each vertex is a point on the 2D plane, so the weight of each edge is the Euclidean distance between the vertices. I am randomly creating a path thru all the vertices and I ...
0
votes
0answers
63 views

Trim graph to minimum

I have an Euclidean graph: each vertex is a point on the 2D plane, so the weight of each edge is the Euclidean distance between the vertices, also all the vertices are connected with edges. I want to ...
1
vote
1answer
125 views

Converting graphs to sets of paths

I have an Euclidean, undirected graph: each vertex is a point on the 2D plane, so the weight of each edge is the Euclidean distance between the vertices. The number of vertices with no edges is ...
11
votes
2answers
700 views

Shortest non intersecting path for a graph embedded in a euclidean plane (2D)

What algorithm would you use to find the shortest path of a graph, which is embedded in an euclidean plane, such that the path should not contain any self-intersections (in the embedding)? For ...
2
votes
1answer
1k views

A* to find the longest path in a directed cyclic graph

I have written an A* algorithm to find the shortest path through a directed cyclic graph. I am trying to modify it to find the longest path through the same graph. My attempt was to write it so that ...
1
vote
2answers
757 views

Shortest path that passes through specific node(s)

I am trying to find an efficient solution to my problem. Let's assume that I have positive weighted graph G containing 100 nodes(each node is numbered) and it is an ...
5
votes
1answer
182 views

Dividing a weighted planar graph into $k$ subgraphs with balanced weight

I've been looking for an algorithm which divides an undirected, weighted, planar and simple graph into $k$ disjoint subgraphs. Here, the graph is sparse, $k$ is fixed, and there are no negative edge ...
2
votes
0answers
232 views

Effect of increasing the capacity of an edge in a flow network with known max flow

I need your help with an exercise on Ford-Fulkerson. Suppose you are given a flow network with capacities $(G,s,t)$ and you are also given the max flow $|f|$ in advance. Now suppose you are ...
2
votes
0answers
52 views

Multicommodity shortest path problem on a directed acyclic graph

I have n commodities with each a unique source and sink node. Each source-sink pair is connected in some manner on a directed acyclic graph. All arc weights are non-negative. The goal is to find the ...
5
votes
2answers
1k views

Modifying Dijkstra's algorithm for edge weights drawn from range $[1,…,K]$

Suppose I have a directed graph with edge weights drawn from range $[1,\dots, K]$ where $K$ is constant. If I'm trying to find the shortest path using Dijkstra's algorithm, how can I modify the ...
6
votes
1answer
507 views

Minimum s-t cut in weighted directed acyclic graphs with possibly negative weights

I ran into the following problem: Given a directed acyclic graph with real-valued edge weights, and two vertices s and t, compute the minimum s-t cut. For general graphs this is NP-hard, since one ...
5
votes
2answers
110 views

An edge that connects more than two nodes in a graph?

Is there a way to create a single edge on a graph that connects 3 or more nodes? For example, let's say that the probability of Y occurring after X is 0.1, and the probability of Z occurring after Y ...
7
votes
1answer
1k views

Do the minimum spanning trees of a weighted graph have the same number of edges with a given weight?

If a weighted graph $G$ has two different minimum spanning trees $T_1 = (V_1, E_1)$ and $T_2 = (V_2, E_2)$, then is it true that for any edge $e$ in $E_1$, the number of edges in $E_1$ with the same ...