Questions tagged [weighted-graphs]
Questions about graphs in which every edge is associated with a weight.
186
questions
2
votes
2answers
92 views
Weight functions in graph algorithms
In text books, for instance in the 3rd edition of Introduction to Algorithms, Cormen, on page 625, the weights of the edge set $E$ is defined with a weight function $w:E\rightarrow \mathbb{R}$.
Why ...
0
votes
0answers
23 views
gas station problem variation
A question from an exam:
Input:
A map of a country with distances (in km) on roads. some
cities have gas stations.
The map is given in the form of directed ...
1
vote
1answer
28 views
Path of exact cost k in DAG
struggling with this question from an exam:
input:
DAG G=(V,E). each edge $e_i$ has weight $w_i\in \text{{0,1,2,3}} $
Two vertices : s,t
Number: k
output:
...
3
votes
0answers
31 views
Alternative criterion for approximate maximum-weight perfect matching algorithms [closed]
Is there any literature on approximate maximum-weight perfect matchings where the approximation criterion is not the factor between the approximate and exact weight sum achieved by each solution, but ...
0
votes
0answers
12 views
Check valid flow in a graph
For a flow network $G=(V,E)$ where $s,t \in V$ and capacities $c_e>0$ for $e \in E$. A flow $f$ is given. How can I check whether of not $f$ is a valid flow within the network?
3
votes
1answer
59 views
Algorithm to compute sum of cost of all path between pair of unique vertices of a tree
Given tree is undirected graph. It has n vertices and n-1 edges. The algorithm should compute the sum of cost of all path between pair of unique vertices.
Thus, there are total nC2 or n(n-1)/2 such ...
1
vote
2answers
38 views
What is the graphic TSP?
I'm not sure if I understand the following definition of the (well-known apparently) Graphic TSP, also known as graph-TSP :
...graph-TSP, that is, the traveling salesman problem where distances ...
3
votes
0answers
65 views
Assign weights to the edges in a DAG so that, for all S and T, all paths from S to T have equal weight
I have a DAG, and on each edge, I have a minimum and maximum weight. I would like to assign (or determine it's impossible to assign) exact weights to each edge so that
Each edge's weight is between ...
0
votes
1answer
33 views
Finding the maximum disjoint weight in a weighted node graph
I have a graph of nodes that reflect resource allocation. Each node has a weight to reflect this. A well formed graph is disjoint, so there will be no edges, and the weight of the graph is just the ...
0
votes
0answers
21 views
Single source shortest paths with even path [duplicate]
Given directed graph with non negative weights and vertex s.
I need an algorithm that finds shortest paths from s to all vertices and the paths have to be even.
1
vote
1answer
53 views
Maximum weight vertex-disjoint paths
I have a complete (every vertex is connected by an edge to every other vertex) undirected positively weighted graph. I want to find vertex-disjoint paths in the graph whose total weight is as large ...
2
votes
3answers
59 views
Shortest path between any origin to any destination through some way stations
How can one find the shortest path between any one of the origins to any one of the destinations through a number of way stations on the way using Dijkstra algorithm?
You can visit those way stations ...
1
vote
0answers
11 views
complexity of computing fractional edge-chromatic number of an edge-weighted graph
Let $(G,w)$ be an edge-weighted graph, where the weights $w(e)$ are assumed to be rational. My question is: What is the complexity of computing $\chi'_f(G,w)$, the fractional edge-chromatic number of ...
1
vote
0answers
66 views
Approporiate algorithm for a graph theory problem
So I have recently ran into a graph theory problem and was unable to find a matching algorithm for the problem or reword the problem to match some existing algorithm.
The problem is pretty ...
0
votes
1answer
43 views
The cheapest path in the graph [duplicate]
I am supposed to decide, if the statement is true or false and use arguments for my answer.
In every weighted n-vertices graphs:
with no negative weighted edges,
with n>10,
in which every weighted ...
0
votes
0answers
36 views
Finding negative cycle using Bellman Ford
Given a graph with |V| vertexes and |E| edges, I have to find a negative cycle, if there is one, in a graph.
The wanted complexity is O(|V|*|E|).
I was thinking about using Bellman-Ford to solve the ...
3
votes
2answers
107 views
Single-source shortest paths with even weight
I need help to find an algorithm that calculates the single-source shortest paths in a graph, with an extra condition that the weight of the path has to be even.
In another words, we have to find the ...
2
votes
2answers
37 views
Uniqueness of minimum spanning tree
If G has a unique minimum spanning tree, does that mean the edge weights in G are also unique? if yes why and if no why?
1
vote
1answer
67 views
Define the time complexity of Kruskal's algorithm as function
I am trying to define the time complexity of Kruskal's algorithm as function dependant on:
the number of vertices V
the number of edges ...
0
votes
0answers
36 views
Real-world scenario for a theoretical problem on trees
Suppose one has a tree with each node weighted with a tuple (say, some fixed $2$ dimensions, for now) of integers. Now we query the tree with two vertices $x$ and $y$ and a range $[a,b]\times [c,d]$, ...
0
votes
0answers
36 views
Whats the time complexity of Prims Algo. without heaps (using priority queue)?
Here's my attempt:
Initialisation -
...
1
vote
1answer
165 views
Djikstra's algorithm to compute shortest paths using at least k edges
I have a graph G = (V, E) where each edge is bidirectional with positive weight. I want to find the shortest path from vertex s ...
1
vote
1answer
130 views
Multiple Source Shortest Paths in a weighted graph
In an unweighted graph, we can find Multiple Source Shortest Paths using the Breadth-First Search algorithm by setting the distance of all starting vertices to zero and pushing them into the queue at ...
3
votes
1answer
79 views
Maximal Minimum Spanning Tree by Removing $k$ Edges
The problem is as follows:
Consider a connected, undirected, and weighted graph $G = (V, E, w)$ and an integer $0 < k < |E| - |V| + 1$. Describe and analyze and efficient algorithm to remove ...
2
votes
1answer
115 views
Given directed connected weighted graph, check if d(v) = delta(s,v)
I'm having some hard time with this problem.
Can someone give me some clue/guidance?
This is an homework question, so please don't just solve it.
Given a weighted directed connected graph $G = (V,...
3
votes
1answer
113 views
Constructing a minimum spanning tree from an all-shortest path graph?
Given an $n \times n$ shortest path distance matrix $D$. And a complete graph $G(D)$ on $n$ nodes, where edge $(i, j)$ has weight $D_{ij}$. Furthermore, the distance matrix $D$ is computed for a ...
2
votes
2answers
132 views
Given all pairs shortest paths matrix, find graph with minimum total sum of edges
I was looking at some problems about graphs, and I got stuck on this one. Namely, we have given matrix of size $N \cdot N$ representing the length of the shortest path in undirected graph between some ...
2
votes
2answers
169 views
Floyd Warshall's All pair shortest path problem does not evaluate all possible paths
We know that the FW all pair shortest path is a Dynamic Programming (DP) approach to solving the problem. Being a DP, it smartly evaluates all possible options before deciding the final option at each ...
3
votes
1answer
83 views
Is maximum edge-weighted triangle-free graph NP-hard?
Given a graph $G$ with weights $w_e$ on the edges, choose a subset $S$ of the ''edges'' such that $S$ doesn't contain any 3-cycles, maximizing $\sum_{e\in S} w_e$.
Is this problem NP-hard? I thought ...
1
vote
1answer
29 views
How is Johnson's shortest path weighting function $\hat{w}(u, v) = w(u, v) + h(u) - h(v)$ proven by the triangular inequility?
Recap to the Johnson's shortest path algorithm:
By the procedure extending the original graph $G^\prime = (V^\prime, E^\prime), V^\prime = V\ \cup \{s\}, E^\prime = E\ \cup \{(s, v)\ |\ \forall v \in ...
1
vote
1answer
68 views
Generating a random minimum spanning tree
I am tring to find the simplest method of generating a random minimum spanning tree.
My intention is to randomly generate a Level in a game where there are n amount of fixed sized rooms existing on a ...
-2
votes
1answer
459 views
Please indicate whether each of the following statements is TRUE or FALSE and provide a brief justification
I provided my answers in the "answer your own question" bit.
I have applied the same logic for my answers to a&b and c&c which seem to be essentially the same questions. Am I right though?
a)...
0
votes
1answer
44 views
More efficient maximum bipartite matching
I've been looking into weighted matching in bipartite graphs and am currently looking at maximum matchings in weighted bipartite graphs. As I've been reading and poking around at different books and ...
3
votes
1answer
71 views
Algorithm for minimizing the number of “inversions” in a graph
Given the following graph:
With the assumptions below:
A node on the left is linked to several nodes on the right
Nodes on the right are paired together: one is black, one is white
Each pair of ...
2
votes
2answers
39 views
Traversing a graph in finite time, maximizing utility
I am working on a problem in robotics, where we have a problem of having finite time horizon T, and a set of actions. Each take some time to perform and each have a utility. We can transition from any ...
1
vote
0answers
176 views
Given a binary tree of leaves with weights, find minimum weights for internal nodes (such that sum(weighti-weightj) is minimized for (i,j)∈E(T))
So this is a question within a bigger question for which I've reduced to this so far:
If I have a tree (phylogenetic) with known weights for leaves, how would I find the weights for all internal ...
1
vote
1answer
33 views
Manber's graph-partitioning implementation
I'm having trouble understanding a part of Manber's graph-partitioning algorithm, presented in A Text Compression Scheme that Allows Fast Searching Directly in the Compressed File.
Generally speaking ...
1
vote
0answers
43 views
Calculate maximum sum of nodes property with limit on distance being traversed between nodes in a given graph
Given is an undirected weighted graph with N nodes, with each node having a property/Value.
Aim is to find the bestpath which maximizes the sum of the nodes property which can be visited given a ...
1
vote
0answers
109 views
How to handle negative edge weights in distance vector routing protocol with a digraph?
In a Distance Vector routing protocol each node implements a Bellman-Ford inspired algorithm that shares it's routing table (Distance Vector) with each of it's incoming links (upstream neighbors). ...
1
vote
1answer
64 views
Finding a minimum weight path with certain restrictions
I have a directed weighted multigraph whose vertices are sets of URLs.
We add to this multigraph all edges of the form $i\to j$ where $i\subset j$ (such edges are of zero weight), where $i$, $j$ are ...
1
vote
2answers
27 views
Representing a network with two types of connections: A fishing application
I want to represent a fishing network using a graph representation. My question surrounds how I can write the adjacency matrix if there are two types of connections, which I want to capture together.
...
6
votes
2answers
191 views
Path in an edge-weighted undirected graph
Is it an $NP$-hard problem?
You're given an undirected graph $G(V,E)$ with edge weight $w: E \to \mathbb{N}$ and a function $\mathrm{max}$-$\mathrm{visit}: V \to \mathbb{N}$ and a number $W$ in unary....
2
votes
1answer
92 views
Path in a vertex-weighted undirected graph
Is it an $NP$-hard problem?
You're given an undirected graph $G(V,E)$ with vertex weight $w: V \to \mathbb{N}$ and a function $\mathrm{max}$-$\mathrm{visit}: V \to \mathbb{N}$ and a number $W$.
Does ...
2
votes
1answer
81 views
Mimimum spanning tree with a constraint on number of certain types of edges
I have the the following problem.
Say we have a graph $G = (V,E)$ where all $e \in E$ have positive weight, and $E$ can be separated in to two disjoint sets $E = A \cup B$. We have to find a spanning ...
2
votes
1answer
22 views
Marginalise edge weights on graph
I have a directed acyclic graph with a score on each edge. The score of a path is defined to be the sum of the scores on the edges along this path. The probability of a path is the score of such a ...
4
votes
0answers
320 views
graph signal processing
What's the intuition behind a ''Graph fourier transform'' ? I'm not so much interested in mathematical details or technical applications. I'm trying to grasp what a graph fourier transform actually ...
0
votes
0answers
95 views
Shortest path between 2 nodes subject to constraints
I am trying to find shortest path between 2 nodes in a graph similar to below:
Each edge has a weight assigned to it. Also, the graph is directional with each edge directing from left to right.
I ...
0
votes
1answer
83 views
Maximize vertex cover weights with bounded edge weights in a connected subgraph
Similar questions were asked elsewhere, but no satisfying answers occurred yet.
In a graph with weights for both vertices and edges, I want to find a subgraph, whose sum of internal edge weights is ...
1
vote
0answers
71 views
Prove an algorithm. Give directed graph edge weights such that weight of every cycle is 0
I need to construct a graph with the following properties:
$w(u, v)$ = $-w(v, u)$, for every edge $(u, v) \in E$
Weight of all $u \leadsto v$ paths is equal, for every $u, v \in V$ (this is zero ...
0
votes
3answers
642 views
Find longest path in graph with N nodes and N edges
We have given weighted undirected connected graph with $n$ nodes and $n$ edges, we want to find the longest path in it. Note that the path should be in each node at most once. Since the graph has $n$ ...
