Questions tagged [weighted-graphs]

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

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Finding min s-t cut of network with flow on the nodes

Given a network with flow on the nodes. How can we find min s-t cut in a network with flow on the nodes? We know how to find min s-t cut whenever there’s a network with flow on the edges (Ford ...
Almog David's user avatar
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35 views

Running time of variant of Dijkstra's algorithm

Consider the problem of finding the shortest-path distances from an origin vertex to all other vertices in a digraph. Normally in Dijkstra's algorithm, we visit the vertex whose shortest distance from ...
Andrew's user avatar
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Bipartite matching with constraints on one part

We have a bipartite graph with parts $A$ and $B$, and it is edge weighted. We have some constraints for part $B$. Each constraint is in this format: Between vertices $b_1$ and $b_2$ both from part $B$,...
Soroush Vahidi's user avatar
1 vote
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25 views

What is the name of this extension of the maximum independent set problem?

Problem: we have an undirected graph. Each vertex $v$ has a weight of $w_v$. For each vertex $v$, a nonnegative number $a_v$ is given, and for each edge $e$, a nonnegative number $b_e$ is given. ...
Soroush Vahidi's user avatar
1 vote
0 answers
57 views

What is the name of this matching problem?

We have a bipartite graph consisting of parts $A$ and $B$. Each vertex $i$ of part $A$ has weight $w_i$ and capacity $c_i$. We say a vertex $i$ in part $A$ is satisfied if at least $c_i$ adjacent ...
Soroush Vahidi's user avatar
3 votes
1 answer
69 views

Path planning on 2D grid graph to maximize the neighboring grid points of a path: Can we do better than brute DFS?

On a finite 4-connected grid graph, given the source point and destination, it is allowed to consecutively move in one of the four orientions (up, down, left or right) to form a path. We get 1 bonus ...
Rabbiiiiit's user avatar
1 vote
1 answer
83 views

Can Rural Postman Problem with arbitrary start and end be reduced to Rural Postman Problem with single depot node?

Can Rural Postman Problem with arbitrary start and end be reduced to Rural Postman Problem with single depot node? The rural postman problem is: Given a weighted MultiDiGraph $G=(V,E)$, a subset of ...
somewhere's user avatar
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1 answer
96 views

How to find maximum number of edge-disjoint trails of length $k$ of a directed multi-graph $G=(V,E)$ between arbitrary start and end vertices?

How to find and return the maximum number of edge-disjoint trails of equal length $k$ of a directed weighted multi-graph $G=(V,E)$ between arbitrary start and end vertices? The start and end vertices ...
IsalanOnkar's user avatar
4 votes
2 answers
61 views

Single Source Shortest Path Problem with Multiple Weights Each Edge

I am trying to solve the single source shortest path problem, but with the added constraint that there is an additional weight on each edge (so we have two weights in total for each edge, call them p ...
Daniel's user avatar
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Can negative edge weights in a graph be positive numbers?

I'm a little confused by the concept of a "negative" edge weight. All of the examples I have seen represent negative edge weights as negative numbers. Is it possible for an edge weight to ...
Daniel's user avatar
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How can I track multiple shortest paths from one node to another using Dijkstra / Bellman-Ford

I want to find how many shortest paths are there from Node A to node B. For example, let's say we have a graph with 3 nodes and 3 connections: from 1 to 2 weight 5 from 1 to 3 weight 11 from 2 to 3 ...
ViktorMaksimoski's user avatar
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Solving a weighted minimum dominating set problem with its unweighted counterpart?

Question Is it possible to find a solution to the weighted minimum dominating set problem, by solving a (related), unweighted minimum dominating set? Elaboration In essence, can one convert a ...
a.t.'s user avatar
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1 vote
1 answer
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Find a weight threshold for edges for maximum number of connected components in a graph

So the problem starts with a graph in which every node is connected with every node by a weighted edge. The goal is to find a weight treshold W, so that every edge that has a weight lower than or ...
Tomyy's user avatar
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Minimum k-cut with equally weighted sets

I've got a weighted graph $G$, where additionally each vertex has a weight too. For a fixed, given $k$ I am looking for an algorithm to partition $G$ into $k$ disjoint sets of vertices, so that: The ...
kchnkrml's user avatar
1 vote
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87 views

Topological sort of DAG that minimizes maximum number of unique-source-edges crossing through any node when placed in 1-d line

Consider a DAG such as one shown below: How do I find a particular topological order of nodes, such that when the nodes are placed in a straight line, the maximum number of unique-edges that cross ...
nepee's user avatar
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1 answer
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Which algorithm solves the single-pair shortest path in a weighted directed cyclic graph?

I need to find the shortest path between two nodes in a directed, positively weighted graph that migt contain cycles. All weights are either zero or one. If it was not weighted, I'd use breadth-first ...
Anna's user avatar
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1 answer
69 views

Directed weighted multigraph with dynamic edges - shortest path

I need to create an implementation of a directed weighted multigraph with dynamic edges: The edges will be changing during the pathfinding, in the following way: Summary of the pathfinding: ...
discrete coder's user avatar
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1 answer
152 views

Find the shortest distance path in a weighted graph, where the weight of each edge is non-negative and less than a constant C = 500 in linear time

The problem is to find the shortest distance in a weighted graph, where the weight of each edge is non-negative and it is given that the weight of each edge is less than a constant C. For example, C = ...
Mikey's user avatar
  • 3
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1 answer
73 views

find the shortest path between two vertices with Dijkstra (Increase and deacrese wieght one by one)

We have a weighted and undirected graph. I want to find the shortest path between two vertices with Dijkstra algorithm. But in the path, the weight of the edges should be increased and decreased one ...
Amir's user avatar
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1 vote
1 answer
185 views

Why Prim algorithm may fail to return minimum spanning forest on disconnected undirected graph

I am trying to address the following claim- "running prim algorithm on a disconnected undirected graph returns minimum spanning forest". I thing that the claim may be false (i.e there might ...
DR_2001's user avatar
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1 answer
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Transforming a Travelling Salesman Problem to a Maximum Clique Problem

Say you have a directed graph consisting of n nodes and containing edge weights. A starting node is also given. You want to begin your route at that node and visit each other node in the graph exactly ...
Emily's user avatar
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1 answer
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How sparsity term in loss function for sparse autoencoder is making hidden units inactive?

I am working on a Sparse Autoencoder but Andrew NG's notes are hard to understand. My question is about the following equation: Loss Function. In sparse autoencoder, the goal is to inactive some ...
p200401Samuel's user avatar
-1 votes
1 answer
253 views

How to show that any greedy algorithm gives a 2-approximation for the best min weighted vertex cover

The problem I am trying to solve is that there is an underlying undirected graph G = (V, E) with weights on the vertices, where the weight on vertex ...
ConScience's user avatar
1 vote
3 answers
122 views

Algorithm to find Minimal Spanning Subgraph

I'm attempting to solve this problem: Given an undirected connected graph $G=(V,E)$ with $\mathrm{weight}(e)>0$ for all $e \in E$, and a subset $S \subseteq V$, we define that a sub-graph $H=(V',E')...
Aishgadol's user avatar
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Analyzing Parallel Matching Algorithm - Why it takes O(n+m) time and work?

Using the algorithm provided by this paper, they said that: The algorithm defines a single phase of the local max algorithm. Each step of the phase takes at most O(log(m + n)) = O(logn) time and O(n +...
Reem Aljunaid's user avatar
1 vote
2 answers
64 views

Shortest path algorithm on graphs with non-numerical weights

TL;DR: Floyd-Warshall algorithm seems to also accept "is-a" and "has-a" relationships as edge weights. I want to know exactly why this is fine, and how to generalize this notion of ...
EatChangmyeong's user avatar
1 vote
0 answers
97 views

Longest (weight-wise) walk In a directed graph with weights becoming negative after traversing once

Problem definition I have a directed graph $G = (V,E)$, with positive weights $w(e)>0\:s.t\:\forall e \in E$ I would like to find the longest walk (i.e. edges and nodes may be repeated) in terms ...
sagooz's user avatar
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2 answers
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MInimum Spanning Tree and Combinatorics

I just got a small confusion here, I have a graph for which i need to get number of minimum spanning tree, So, in graph i have 3 edges with weight 2 and 4 edges with weight 3, in such a way that AE = ...
Niraj Jain's user avatar
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2 answers
174 views

subtract the weight of the largest edge

I have an oriented and weighted graph, and I need to find the cheapest route from source to destination. Now I have a source node A and a destination node B the cheapest path is given to me by the sum ...
ant0982's user avatar
  • 13
2 votes
1 answer
125 views

Minimize max subtree weight among spanning trees

Suppose we have an undirected, connected graph $G$ where vertices have positive integer weights. Let $\bar{v}$ be a given vertex in $G$. Take a spanning tree $T$ of $G$ rooted at $\bar{v}$ and define ...
Andrew's user avatar
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1 answer
110 views

Algorithms for finding closest graph node within set of nodes

Given a set of nodes $N$ on an undirected, weighted graph $G$ and a query node $n$, what is the fastest algorithm for finding the node in $N$ that is closest to $n$? Furthermore, say we are doing many ...
user12878817821's user avatar
-1 votes
1 answer
35 views

Is there an algorithm able to finding the best cost in a graph that is weighted on both vertices and edges?

I have a problem that consists of finding a good solution for a graph that has vertex weights (and this cost is the highest priority), but also has edge costs.
Fernanda's user avatar
-1 votes
1 answer
92 views

Does a minimum spanning tree necessarily provide the lowest cost path between any 2 nodes?

If I'm given a minimum spanning tree, my understanding is that it is a structure that connects all nodes to each other through some path, and that the overall weight of the tree is smallest. However, ...
Jeremy Fisher's user avatar
3 votes
1 answer
102 views

Efficiently determine which nodes should leave a graph while maintaining connectedness

Suppose I have a graph with node weights, where a weight is either -1 or a positive integer. For example: If a node has weight -1, it is "happy", and cannot be kicked out of the graph. If a ...
416E64726577's user avatar
-1 votes
1 answer
31 views

weighted graph separation algorithm proof

I have a graph G (G=(V,E)), where each edge has a non negative weight to it. My problem is to find a subset S (it doesn't have to exist) of nodes such the sum of all the weights of the edges that ...
Johnny13696's user avatar
0 votes
2 answers
302 views

Calculate shortest cycle that contains node $s$

Let $ G(V,E,w)$ be a graph with no negative weights. Describe an algorithm that returns the shortest cycle containing a node $ v $. I came across this algorithm https://courses.engr.illinois.edu/cs374/...
Danny Blozrov's user avatar
0 votes
1 answer
129 views

Dynamic routing algorithm

In static routing where the network parameters dont change, we can use Djikstra's or Bellman-Ford's algorithm to find the shortest path to send data from source to destination.However in dynamic ...
Jun Seo-He's user avatar
1 vote
1 answer
133 views

Subpath optimality lemma in weighted undirected graphs

In an introductory course on Dijkstra's algorithm, I enunciated the following lemma : Let x →* z be a shortest path in a weighted graph and let y be any vertex along that path. It follows that x →* y ...
ysalmon's user avatar
  • 233
1 vote
1 answer
73 views

Subdivide a graph into non-crossing triangles with maximum edge weight

Let $G=(V,E)$ be a complete finite graph with the vertices arranged in a circle. Each edge has a nonnegative weight, and we would like to find an efficient algorithm to find a subgraph of maximum ...
Addem's user avatar
  • 313
0 votes
1 answer
239 views

Tweaking Floyd-Warshall Algorithm to detect cycles

Cheers, I am trying to solve the problem of minimum length cycle in a graph, and I came across a solution that suggested that I should tweak the Floyd-Warshall algorithm to solve that. It stated that ...
average_discrete_math_enjoyer's user avatar
3 votes
1 answer
323 views

Is there an efficient algorithm to find GCD of all cycles' lengths in directed multigraph?

I have weighted connected directed graph with cycles which can have multiple edges and loops (edge from vertex back to itself). Weight of each edge is its length (always positive integer). There ...
Somnium's user avatar
  • 275
0 votes
0 answers
241 views

bellman ford and dijkstra sparse vs dense graphs

I believe using big o notation that Bellman-Ford is to be expected to be faster on sparse graphs and dijkstra's should be expected to be faster on dense graphs, but in practice dijkstra's is always ...
csstudent3423's user avatar
0 votes
0 answers
36 views

Updating Shortest Path Weight from One Destination to Another

Let $G=(V,E)$ be a directed graph with possibly negative edge weights. Given a destination $t$. Suppose that we have already known $d_v$, the shortest path weight from $v$ to $t$. If I'd like to ...
Hang Wu's user avatar
  • 121
1 vote
1 answer
48 views

Why do we round from 1/2 when converting the LP to ILP for the weighted vertex cover problem?

I understand that to approximate a solution to the weighted vertex cover, we need to relax the integer linear program to a linear program which can be solved in polynomial time, but why do we round ...
Insanit's user avatar
  • 13
2 votes
0 answers
72 views

Translating weighted regular expressions with the complement operator to weighted deterministic automata

I want to implement regexp search via translation to deterministic automata, as a toy project. TLDR: how to combine the extended regular expressions with the weighted regular expressions, with the ...
user2373145's user avatar
2 votes
3 answers
1k views

Determines if the minimum spanning tree only uses edges with an integer weight, when E, V are in O(n)

Given a undirected graph $G=(V,E)$ with $|V|=n$ and $|E|=2022n$ and some weight function $w\colon E\to \mathbb{R}$, and $0≤ w(e) ≤n$ for all $e∈E$, Describe an algorithm that determines if the MST ...
Saar BK's user avatar
  • 55
2 votes
1 answer
150 views

Spanning tree that maximizes all-pairs bandwidth => Maximum spanning tree?

Let $G = (V, E)$ be a weighted, undirected graph, with $f: E \to \mathbb{R}$ its weight function. Given a path $P = (e_1, \dots, e_k)$, we call $\operatorname{bwd}(P) = \min_{1 \le i \le k} f(e_i)$ ...
Federico Lebrón's user avatar
1 vote
0 answers
196 views

Clash Royale Algorithm for troops path

I am making a clone of Clash Royale which is basically a Tower Defence game. As you can see from the picture you can deploy different troops only in your side of the court (that blue rectangle), and ...
panini's user avatar
  • 19
1 vote
1 answer
379 views

How to find the lightest path that has at least one vertex of each color?

I've faced this question in my homework. In a graph $G=(V,\ E)$ where every $v\in V$ has a color, a colored path is a path such that it has at least one vertex of each color. We're given a directed ...
Mohamad S.'s user avatar
1 vote
0 answers
17 views

Aggregating pairwise ratings in a graph

A finite set of individuals provide bounded non-binary pairwise ratings of other individuals (say, -10 to +10), forming a directed graph (cycles possible). I'd like to determine aggregate ratings for ...
vsekhar's user avatar
  • 111

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