Counting shortest paths in a non-directed graph using BFS

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SUMMARY

The discussion focuses on calculating the number of shortest paths between two nodes in a non-directed graph using Breadth-First Search (BFS). The proposed algorithm operates in linear time, specifically O(n + m), where n represents the number of vertices and m represents the number of edges. Participants emphasize the importance of counting nodes during the BFS queue operations to determine the number of shortest paths efficiently. Implementing this algorithm is encouraged to validate its effectiveness and measure its complexity.

PREREQUISITES
  • Understanding of non-directed graphs and their properties
  • Familiarity with Breadth-First Search (BFS) algorithm
  • Knowledge of graph theory concepts such as vertices and edges
  • Basic algorithm complexity analysis
NEXT STEPS
  • Implement the BFS algorithm to count shortest paths in a non-directed graph
  • Explore advanced graph algorithms such as Dijkstra's algorithm for weighted graphs
  • Study graph representation techniques, including adjacency lists and matrices
  • Learn about graph traversal techniques and their applications in real-world scenarios
USEFUL FOR

This discussion is beneficial for computer scientists, software developers, and algorithm enthusiasts interested in graph theory and efficient pathfinding techniques.

evinda
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Hello! (Wave)

A non-directed graph $G=(V,E)$ and two nodes $v$ and $u$ of $G$ are given. Give an algorithm that calculates the number of shortest paths $v-u$ in $G$. (The algorithm doesn't have to print all the paths, just how many exist.) The algorithm should run in time $O(n+m)$ for a graph with $n$ vertices and $m$ edges. Is it like that?

We apply BFS. At the point where we add the nodes in the queue, we calculate also the number of nodes.
 
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What do you think? Have you tried implementing it to see if it sort of works, try and measure the complexity, ...?
 

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