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Questions tagged [shortest-path]

Shortest path problems are problems addressing finding the shortest path from a single source to a target source, usually in a graph.

Shortest path problems are problems addressing finding the shortest path from a single source to a target source, usually in a graph.

Some of the commonly used shortest path algorithms are:

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Why doesn't Dijkstra's algorithm work for negative weight edges?

Can somebody tell me why Dijkstra's algorithm for single source shortest path assumes that the edges must be non-negative. I am talking about only edges not the negative weight cycles.
Madu
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How does a Breadth-First Search work when looking for Shortest Path?

I've done some research, and I seem to be missing one small part of this algorithm. I understand how a Breadth-First Search works, but I don't understand how exactly it will get me to a specific path, as opposed to just telling me where each…
Jake
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Negative weights using Dijkstra's Algorithm

I am trying to understand why Dijkstra's algorithm will not work with negative weights. Reading an example on Shortest Paths, I am trying to figure out the following scenario: 2 A-------B \ / 3 \ / -2 \ / C From the…
Meir
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Knight's Shortest Path on Chessboard

I've been practicing for an upcoming programming competition and I have stumbled across a question that I am just completely bewildered at. However, I feel as though it's a concept I should learn now rather than cross my fingers that it never comes…
Kyle Hughes
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Bellman-Ford vs Dijkstra: Under what circumstances is Bellman-Ford better?

After a lot of Googling, I've found that most sources say that the Dijkstra algorithm is "more efficient" than the Bellman-Ford algorithm. But under what circumstances is the Bellman-Ford algorithm better than the Dijkstra algorithm? I know…
crazyCoder
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A* Algorithm for very large graphs, any thoughts on caching shortcuts?

I'm writing a courier/logistics simulation on OpenStreetMap maps and have realised that the basic A* algorithm as pictured below is not going to be fast enough for large maps (like Greater London). The green nodes correspond to ones that were put…
drspa44
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What is difference between BFS and Dijkstra's algorithms when looking for shortest path?

I was reading about Graph algorithms and I came across these two algorithms: Dijkstra's algorithm Breadth-first search What is the difference between Dijkstra's algorithm and BFS while looking for the shortest-path between nodes? I searched a lot…
harrythomas
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Using BFS for Weighted Graphs

I was revising single source shortest path algorithms and in the video, the teacher mentions that BFS/DFS can't be used directly for finding shortest paths in a weighted graph (I guess everyone knows this already) and said to work out the reason on…
user2125722
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How to calculate the shortest path between two points in a grid

I know that many algorithms are available for calculating the shortest path between two points in a graph or a grid, like breadth-first, all-pairs (Floyd's), Dijkstra's. However, as I noticed, all of these algorithms compute all the paths in that…
Alan_AI
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Finding all the shortest paths between two nodes in unweighted undirected graph

I need help finding all the shortest paths between two nodes in an unweighted undirected graph. I am able to find one of the shortest paths using BFS, but so far I am lost as to how I could find and print out all of them. Any idea of the…
user1946334
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Dijkstra vs. Floyd-Warshall: Finding optimal route on all node pairs

I am reading up on Dijkstra's algorithm and the Floyd-Warshall algorithm. I understand that Dijkstra's finds the optimal route from one node to all other nodes and Floyd-Warshall finds the optimal route for all node pairings. My question is would…
pyt
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What is the difference between Dijkstra and Prim's algorithm?

Can any one tell me the difference between Dijkstra's and Prim's algorithms? I know what each of the algorithms do. But they look the same to me. Dijkstra's algorithm stores a summation of minimum cost edges whereas Prim's algorithm stores at most…
Pradit
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What is meant by diameter of a network?

The diagram shown on this link of the "A graph with 6 vertices and 7 edges where the vertex no 6 on the far-left is a leaf vertex or a pendant vertex." has DIAMETER 4? right or wrong? Definitions are The diameter of a graph is the maximum …
user287745
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AStar - explanation of name

I am looking for an explanation why the AStar / A* algorithm is called AStar. All similar (shortest path problem) algorithms are often named like its developer(s), so what is AStar standing for?
lale liley
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Finding kth-shortest paths?

Finding the shortest path between two points in a graph is a classic algorithms question with many good answers (Dijkstra's algorithm, Bellman-Ford, etc.) My question is whether there is an efficient algorithm that, given a directed, weighted…
templatetypedef
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