Questions tagged [shortest-path]

Questions about the algorithmic problems of finding shortest paths between nodes in a graph.

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524 views

Bellman-Ford parent pointer (?) negative cycle

First of all, let me preface by saying that this question is not completly new but the original question hasn't been answered. More important, this is only basic question on understanding the proof ...
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11 views

Queries on unbounded knapsack

Given $n$ types of items with integer cost $c_{i}$ (there is an unlimited number of items of each type), such that $c_{i} \leq c$ for all $i = 1, 2, \dots, n$, answer (a lot of) queries of form "is ...
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15 views

Finding multiple paths through a grid such that every grid square is equally used

Setup Here’s the setup: I have an $N$ x $N$ grid of tiles, and a list of $M$ agents that need to move across the grid. Each agent has its own start tile $S(a)$, end tile $E(a)$, and an exact number ...
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1answer
28 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 ...
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1answer
28 views

Dijkstra shortest path yields unintuitive results

Considering the following nodes with edge weights in red, Dijkstra's shortest path algorithm seems to return incorrect results, at least by the definition of the steps on wikipedia. By those rules, ...
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144 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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120 views

C++ finding the shortest path, reducing time complexity, dijkstra v Floyd Warshall Algorithm?

I have an algorithm that I am performing on a graph and I am looking to do an analysis of how to speed it up and would appreciate any comments. The algorithm iterates over every edge in the graph. ...
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47 views

Can the shortest path problem be solved using Monte Carlo Tree Search?

I think Monte Carlo Tree Search could be used to find the shortest path, but it seems that this method is only used considering win/lose outcomes in the simulation step. If we consider the path ...
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1answer
158 views

Minimum distance of nodes from a set of two nodes

In an unweighted tree, suppose that we want to delete (or mark) any node which is closer to node $v$ than node $w$ ($dist(x,v) < dist(x,w)$). The solution that comes to my mind is running two BFS, ...
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39 views

Concurrent Shortest Paths with “Congestion Penalty”

Given a graph with positive edge weight representing "time to travel through", and 2 or more pairs of start/end vertices, we can find concurrent paths for the pairs such that the maximum cumulative ...
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1answer
44 views

What happens if I replace $<$ with $\le$ in Dijkstra's algorithm?

The following is Dijkstra's algorithm for finding the shortest path in a graph. I know something wrong happens if I replace d[u] + weight(u,v) < d[v] with ...
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1answer
1k views

Behaviour of Dijkstra in Case of Negative Edge Weight [duplicate]

I came across a serious doubt regarding the implementation of the Dijkstra algorithm and hence wanted to discuss. For the given below graph What should be the Cost to reach Node G from Source Vertex ...
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52 views

Finding simple min-weight path between two vertices in graph with negative edge weights

Given a weighted graph (negative weights are allowed) and two vertices $u$ and $v$, can we find the simple min-weight path between $u$ and $v$? There can be a negative cycle on the path from $u$ to $v$...
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133 views

Minimizing cost of shortest paths to a group of vertices by adding minimal edges to an unconnected vertex

Let $G=(V,E)$ be directed graph, where the weights of the edges are non-negative. The graph might have cycles, but without parallel edges. Consider a $T \subset V$, and $u \notin V$. I'm trying to ...
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210 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). ...
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22 views

Why does the inequality $d[v_i] \ge d[v_i−1] + w(v_i−1, v_i)$ hold when all vertices are labelled with their shortest path values upon?

Let $G = (V, E)$ be a weighted, directed graph with weight function $w : E \to R$, and let $s \in V$ be a source vertex. Assume that G does not contain a negative cycle reachable from $s$. Then, if we ...
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23 views

Shortest curve interpolating points with a constraint on the curvature

I'm looking for a method for determining a path for a UAV that interpolates a set of input locations, with a constraint on maximum curvature and given an initial velocity vector. The cost (length) of ...
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1answer
421 views

Find a path that contains specific nodes without back and forward edges

I have a directed graph and and a set of nodes(set = [1,2,5,9,24...]). I want to find a path that contains all the set of nodes and this path dont contain back edges(cycles) and forward edges. For ...
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295 views

Analysing Dijkstra Algorithm by using different varieties of Data Structure

Question I want to analyse Dijkstra Algorithm by using different varieties of Data Structure. My solution Adjacency matrix to Store the Graph and Binary heap for Priority Queue. $...
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49 views

DAG Shortest Path — original citation for academic paper

I am writing to see if someone can point me to the original citation (assuming that a single work can be pointed to) for the single-source shortest path problem in directed-acyclic graphs (DAGs). ...
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354 views

Shortest path with minimal blue edges

Let $G=(V,E)$ be an undirected graph,such that ever $e\in E$ has a color-blue or red. Given $G$ and some $s,t\in V$ ,find an efficient algorithm that find from all pathes from $s$ to $t$,one with ...
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2k views

How to backtrack the shortest path in BFS based shortest path calculation? [closed]

I understand how BFS can give the shortest path in a graph but I am not able to code the entire thing. The part where I am stuck is when I pop a node from the queue and see that its the target node, ...
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54 views

Pathfinding when the graph varies over time

Let's say I want to simulate a very large number of travelers booking flights. For example, a traveler might want to fly from New York to New Delhi. There's no direct flight from New York to New Delhi,...
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591 views

Edge weight changing during execution in shortest path algorithm

I have an undirected graph with weighted edges, in which I want to find the shortest paths from an initial node to every other node. Obviously Dijkstra's algorithm is usually a good choice, and I have ...
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164 views

State-of-the-Art techniques on dynamic shortest path computations

Suppose that I would like to find the shortest path between two vertices in a dynamic graph, where the cost function of an edge changes occasionally. I understand that an efficient algorithm to target ...
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1answer
509 views

Bellman-Ford: Find all nodes that have minus infinite distance to source

Given a weighted, directed graph (V, E) may contains some negative cycles and a source node s, I would like to know for all node ...
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803 views

Correctness of Dijkstra's algorithm

This question is about the correctness proof of Dijkstra's algorithm in the third edition of Introduction to Algorithms by Cormen et al. (pages 660–661). The proof makes a case that considering path $...
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17 views

Optimal linking in synchronous environment for shortest path tree problem

I am dealing with the Shortest path tree problem in the specific synchronous environment. In the following algorithm, initiator begin the execution calling primitives ...
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0answers
112 views

How do I apply a single iteration of Floyd's algorithm to an adjacency matrix? [closed]

I have the following adjacency matrix for a graph with nodes {a,b,c,d}: \begin{bmatrix} & & a& b& c& d\\ & & & & & \\ a& & 0& 1&...
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23 views

Finding next lightest path [duplicate]

Using Dijkstra algorithm, how can I find the next shortest path in a directed weighted graph? (When saying next, I mean that the next path must be heavier than the lightest path and not equal). The ...
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130 views

Weighted, Acyclic Graph and Change Weights Problem?

I ran into a question as follows: We have a Code on Weighted, Acyclic Graph G(V, E) with positive and negative edges. we change the weight of this graph with ...
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103 views

Fully dynamic k-shortest-path

I have a directed acyclic graph with positive edge weights. It is constantly changing in that nodes are deleted and added. For each change, I need to find the $k$ shortest paths. My current approach ...
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56 views

How to convert a search solution to a path to be tracked?

Let's say I have a space with obstacles and I'm trying to control a robot's movement while avoiding obstacles. I also have a start state and a goal state. I use a search algorithm to find the shortest ...
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1answer
766 views

find the shortest path between two nodes where the number of edges is minimal [closed]

Say you are given an undirected unweighted graph, where s and t are nodes from the graph. d(s,t) means the distance between s and t which outputs the number of edges. How do I find the the maximum ...
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0answers
352 views

Influence of edge number and priority-queue implementation on the runtime of Dijkstra

When we try to find the shortest path of a directed weighted graph using Dijkstra’s algorithm, is there a relation between the number of edges/vertices of the graph and the different implementations ...
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0answers
452 views

Parallel single source shortest path algorithm

Is there a deterministic parallel single-source shortest path algorithm (for graphs with non-negative edge-weights) that runs in sublinear time? The number of processors may depend on $n$ or $m$ (i.e.,...
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0answers
93 views

Shortest path with min-sum multiplication and Boltzmann distribution

My professor presented a method to find shortest paths using the min-sum multiplication and Boltzmann distribution. He multiplies the adjacency matrix many times and takes the $\beta$ of Boltzmann ...
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2answers
134 views

Shortest path with a given condition

The problem says to find the shortest way (the smallest amount of intermediary points), with given source and destination points, such that between two consecutive intermediary points there are two ...
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1answer
322 views

Find shortest path in undirected graph that goes through all vertices and returns to starting vertex

I have an undirected weighted graph like this one My task is to find the fastest path (with least weight) that goes from specified vertex goes through all vertices and returns to the starting vertex ...
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2answers
409 views

Can Inverse of weights(1/weight,not negation) be used to find the longest path between two points by using dijkstra's algorithm?

Considering that there no cycles in the graph. I have seen the posts where the negation of the weights is suggested and to use Bellman-ford. But I was wondering if the inverse is possible.
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1answer
36 views

Why does A* fail to find the fastest path when it reaches the goal?

I'm trying to understand how A* works on some simple examples, and something struck me as odd. I could fairly easily come up with situations in which A* "failed". Here is an example: Take a 2x2 grid, ...
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3answers
832 views

Modification of Dijkstra's algorithm

How to modify Dijkstra's algorithm, for wheel chair users, to take into account the road quality? There are three levels of quality: $1$ for pure concrete, $2$ for partly concrete and $3$ for rough ...
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2answers
537 views

Existence of shortest path in a graph with no negative cycles?

Suppose that the input graph $G$ does not have any negative cycles but however it is permitted to contain edges having negative weight. Let $s$ be the source vertex. How do I prove that for every ...
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2answers
662 views

Bellman–Ford negative path meaning

In the Bellman–Ford algorithm, what is the practical meaning of having a negative path between routers? I have tried searching the net but didn't find any data thanks Eli
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2answers
4k views

How to construct the found path in bidirectional search

I am trying to implement bidirectional search in a graph. I am using two breadth first searches from the start node and the goal node. The states that have been checked are stored in two hash tables (...
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2answers
282 views

Shortest distance from multiple points to one point

I am looking for an algorithm to find the shortest distance from multiple nodes to one end node. For example let $v_1,v_2,\dots,v_r$ be the nodes on a graph with distance $d_1,d_2,\dots,d_r$ to the ...
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2answers
1k views

Shortest path in a maze where you can break one wall

How would I solve the following problem? You have maps of parts of the space station, each starting at a prison exit and ending at the door to an escape pod. The map is represented as a matrix of 0s ...
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1answer
582 views

Why does Dijkstra's algorithm not account for updating node distances after expanding a node?

Why does Dijkstra's algorithm not re-evaluate/re-expand nodes who have been expanded and later had their weight changed? For example, in the accepted answer of this question (link), if the algorithm ...
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1answer
2k views

Normalizing edge weights and the effect on Dijkstra's algorithm [duplicate]

If I had a graph $G$ with some negative edge weights, clearly Dijkstra's algorithm does not definitely halt, since it might get caught in a negative cycle (shedding infinite weight). However, would ...
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1answer
3k views

How to optimize Dijkstra's algorithm for a grid graph?

I'm trying to apply Dijkstra's algorithm to the Problem 83 on projecteuler.net. The problem reads: In the 5 by 5 matrix below, the minimal path sum from the top left to the bottom right, by ...

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