Questions tagged [weighted-graphs]

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

85 questions with no upvoted or accepted answers
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12
votes
0answers
646 views

Optimal meeting point in directed graph

Let $G(V, E)$ be a edge-weighted directed connected graph and $v_1, \dots, v_n \in V$ be some vertices. Let $d(a, b)$ denote the length of the shortest path from $a$ to $b$, for $a,b \in V$. I need ...
10
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0answers
216 views

Minimum edge deletion partitioning of a planar graph

I'm interested in the time complexity of the following problem: Given an undirected planar graph $G=(V,E)$ and a weight function $w:E \rightarrow \mathbb{Z}$ (so weights can be negative, too), color ...
5
votes
0answers
634 views

Faster maximum weight matching algorithm in bipartite graph

I need to do a maximum weight matching in bipartite graphs rather than maximum weight perfect matching (which means that there is no need to match all the nodes). The nodes each side are both (at ...
4
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0answers
369 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 ...
4
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0answers
366 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 ...
3
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0answers
47 views

Total weight of all spanning trees

Given a weighted simple undirected connected graph $G = (V, E, w:E \to \mathbb{R})$, let $\tau(G)$ be the set of all its spanning trees. Is there an efficient algorithm to determine or estimate with ...
3
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0answers
108 views

Time taken by virus to reach all nodes

Given a connected graph, with weighted edges, a virus starts from a given node. It takes x seconds for the virus to travel from a node to one of its neighbours where x is directly proportional to the ...
3
votes
0answers
94 views

Dynamic all pairs shortest path edge removal

I have a planar(|E|=O(V)) undirected graph with positive edge weights. I have already calculated all pairs shortest path with Floyd–Warshall algorithm. Now I want to recalculate APSP with an edge ...
3
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0answers
68 views

Assignment problem with symmetric matrix

I came across a problem which I think can be reduced to the assignment problem/Hungarian algorithm. We have matrix $A$ and matrix $B$ which are both $n\times n$ symmetric matrices. We can rearrange $...
3
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0answers
118 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 ...
3
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0answers
129 views

How to find an optimal sequence of matching

Given a graph $G(V.E,w)$ Here $w: E \mapsto R$. We need to find optimal set of matchings(set of edges that have no common vertices) and $t_i$'s such that after all these matchings, it results in $\...
3
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0answers
83 views

Algorithm for finding the set of minimum coordinate pairs

Consider these two sets of coordinate pairs with weights: ...
3
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0answers
422 views

Assigning edge weights under shortest path constraints

We are given a graph $G = (V,E)$ and we need to find an assignment of non-negative edge weights (You must give every edge a non-negative weight). We are also given a set $R\subseteq V$ and mapping $c_{...
3
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0answers
4k views

Applications of min spanning trees

What are the significant applications of minimum spanning trees? After doing some research online and in several textbooks, I have found three real-world applications: Building a connected network. ...
2
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0answers
40 views

Minimum Product Weight in a Graph with 2 weight functions

Hello Community, Given an undirected graph G = (V,E) where E has 2 weight functions w1(e) --> {1,2,..9} and w2(e) --> {1,2...9} with given a source vertex s and destination vertex t. we can ...
2
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0answers
61 views

Matching of two weighted graphs allowing one-to-many mapping

I am looking for a heuristic for a graph matching problem as follows. Given two graphs: $A$ (consisting of nodes $a_i$) and $B$ (consisting of nodes $b_i$). Typically the size of $B$ is larger than ...
2
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0answers
238 views

Maximum number of not overlapping cycles in an undirected graph

Basically, when given an Undirected graph, the problem of getting maximum cycles is known. This case is quite different. The graphs I'm dealing with are made by converting geometric polygons to ...
2
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0answers
494 views

Online version of bellman-ford algorithm?

Suppose I have a graph on which I've run the Bellman-Ford algorithm. Now I change the weight of subset of edges. Is there an efficient way to re-run the algorithm without having to completely start ...
2
votes
0answers
440 views

Bhandari Algorithm: Canceling Edges

I have a quick question on implementing the Bhandari algorithm. I do not have the textbook where the algorithm is originally given (Bhandari, Ramesh (1999). Survivable networks: algorithms for ...
2
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0answers
46 views

Bus stops problem

I have the following problem I need to solve, and I hope you can point me to the right direction. I have a bunch (4000) of people addresses in a city that are mapped to coordinates (longitude and ...
2
votes
0answers
314 views

What is a semantic cognitive map

Based on: J. P. Carvalho, "On the Semantics and the Use of Fuzzy Cognitive Maps in Social Sciences" (WCCI, 2010 -- PDF) and Richard Dagan's web page Cognitive Mapping. A cognitive map consists of ...
2
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0answers
150 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 ...
1
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0answers
28 views

Finding path with best distance/cost ratio from a node in a graph

We have a weighted graph, where each node is a city. And the edges between the nodes are a pair of floating-point values (distance and cost of travel). Given a node/city, describe an algorithm that ...
1
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0answers
15 views

Finding a cut maximizing average weight of cut edges

Just checking if this version of Max Cut is still NP-hard: Given a fully connected graph $G(V,E)$, where every vertex is connected to every other vertex, and where every edge has a weight associated ...
1
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0answers
33 views

“Second order” widest path problem

Let's say we have a directed graph in which each pair of adjacent edges has a weight; or, alternatively, each ordered triple of vertices A, B, C has a weight $W(A,B,C)$ of going A->B->C. I am ...
1
vote
1answer
39 views

how to find all negative weight cycles(elementary circuit) in a strongly connected directed graph?

I can use Bellman-Ford to get some of the elementary negative weight cycles in a graph. It's not guaranteed to always get all of them. (Elementary Cycle: A cycle is elementary if no vertex but the ...
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0answers
18 views

finding common navigational paths / central nodes within a graph

I have a directed weighted graph representing street (edges weighted by distance) and street intersections (nodes). Using this graph, I would like find central nodes that a person might find ...
1
vote
1answer
40 views

Is there such a problem as b-Matching with different b values?

Consider a bipartite Garph $G=(L \cup R, E)$. Naturally, a b-Matching problem is to find a set of edges $M \subset E$, such that each node in $L$ and $R$ are adjuscent to maximum $b$ neighbors, and a ...
1
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0answers
16 views

Number of graphs that satisfies the property that edge weight is maximum of node values on which the edge is incident

I have an undirected weighted graph without multi edges. All the edge weights are whole numbers and known. I want to know in how many ways node values(node values are also whole numbers) can be ...
1
vote
1answer
459 views

Updating a mst after increasing the weight of an edge in the mst

Suppose we have a weighted undirected graph $G$ and a minimum spanning tree $T$ Let $G2$ be a new graph by increasing the weight of one edge $e = (a,b)$ that is part of $T$. I'm using a common ...
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0answers
21 views

Floyd's Algorithm with a negative cycle

I know that I cannot use Floyd's algorithm if I have a graph with at least one negative cycle, because path-lengths between vertices can be arbitrarily small. I am wondering, how the distance ...
1
vote
1answer
57 views

A pathfinding algorithm for graphs in which arc weights can change over time

So I'm not really sure even what to be googling for solutions to this. Hence this question, hopefully, someone can point me in the right direction. Here's the situation, I have a weighted undirected ...
1
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0answers
55 views

What are the common practices to weight tags relations?

I am working on a webapp (fullstack JS) where the user create documents and attach tags to them. They also select a list of tags they are interested in and attach them to their profile. I am not a ...
1
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0answers
416 views

Remove a vertex from a graph keeping shortest path distance same

How could we delete an arbitrary vertex from a directed weighted graph without changing the shortest-path distance between any other pair of vertices? We are allowed to reweight the edges.
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0answers
31 views

Ordering vertices of graph based on specific vertex-transitivity

Given any complete directed weighted graph $G$ with $n$ vertices and matrix of non-unique weights $W$, find a weak ordering $T(G, W)$ on the vertices of the graph satisfying the following conditions: ...
1
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0answers
16 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 ...
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0answers
70 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 ...
1
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0answers
342 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 ...
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0answers
62 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
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0answers
257 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
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0answers
123 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 ...
1
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0answers
139 views

How to find the path for the most negatively-weighted cycle which goes through a specific source node?

I am trying to find the path for the most negative cycle in a graph G which starts and ends at a specified source node S. I have studied an application/ extension of the Bellman-Ford algorithm (...
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0answers
157 views

Bidirectional Search on possible negative weight edges digraphs

There are plenty material about bidirectional search with non-negative edge weights. One example is this paper. I am looking for any improvements using a bidirectional approach for acyclic digraphs ...
1
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0answers
463 views

Dijkstras Algorithm with Bounded Integer Edge Weights

I don't really understand how we can use the fact that the edge weights are integers in the range [1, 2, ... , C] in order to speed up the computation of Dijkstra's algorithm. I read this lecture but ...
1
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0answers
75 views

Polynomial LP-based algorithm for cost minimization of DAG weights modification

Given a DAG $G=(V,E)$, with non-negative weights $ w_e \, \forall e\in E$, we want to modify (increase/decrease) the weights such that: $\forall u,v\in V$ and $\forall p_1\neq p_2 $ paths from $u$ to ...
1
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0answers
493 views

Can I change the order of iteratorion in the Floyd-Warshall Algorithm?

I am studying how Floyd-Warshall works and came across this doubt. In the code: ...
1
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0answers
180 views

Maximum weighted antichain over a DAG with cardinality constraint

Let $G=(V,E)$ be a vertex weighted DAG (Directed Acyclic Graph), with positive real valued weights. Let also $k\leq \left\vert V\right\vert$, is there any way to find a maximum weighted antichain ...
1
vote
0answers
89 views

Branch clustering for an MST

I am working in image segmentation with super pixels. My data is a large matrix describing various attributes of each stick of pixels (such as height, width and disparity). The data comes from an ...
1
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0answers
161 views

Minimal connected subgraph containing 4 specific vertecies

Let $G$ be an undirected weighted connected graph with non-negative weights on the edges, and let $v_1, v_2, v_3, v_4$ be 4 vertecies in $V[G]$. The goal: find a connected subgraph of $G$ with ...
0
votes
0answers
18 views

What is the significance of Bellman-Ford and linear programming for scheduling and makespans?

CLRS exercise 24.4-9 says the following: Show that the Bellman-Ford algorithm, when run on the constraint graph for a system $Ax \leq b$ of difference constraints, minimizes the quantity $\max_i\{x_i\...