# A O(E) Time Shortest Path Algorithm For Non Negative Weighted Undirected Graphs

## TL;DR

This paper introduces a simple, efficient O(E) time algorithm for finding shortest paths between two nodes in nonnegative weighted and unweighted undirected graphs, optimized for scenarios where only specific source-destination paths are needed.

## Contribution

It presents a novel O(E) time algorithm tailored for quick shortest path computation between two nodes in undirected graphs with nonnegative weights, avoiding complex data structures.

## Key findings

- Algorithm runs in O(E) time for most graphs.
- It is simple to implement without complex data structures.
- Effective for targeted shortest path queries in large graphs.

## Abstract

In most of the shortest path problems like vehicle routing problems and network routing problems, we only need an efficient path between two points source and destination, and it is not necessary to calculate the shortest path from source to all other nodes. This paper concentrates on this very idea and presents an algorithm for calculating shortest path for (i) nonnegative weighted undirected graphs (ii) unweighted undirected graphs. The algorithm completes its execution in O(E) for all graphs except few in which longer path (in terms of number of edges) from source to some node makes it best selection for that node. The main advantage of the algorithms is its simplicity and it does not need complex data structures for implementations.

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Source: https://tomesphere.com/paper/0911.0174