Graph algorithms are fundamental in computer science and are widely used in various applications like network routing, scheduling, and project management. This post compares four key algorithms for finding the shortest paths in graphs: <a href="https://github.com/sharathone23/dsa/blob/main/nonlinear/UndirectedGraph.java#L39">Breadth-First Search (BFS)</a>, <a href="https://github.com/sharathone23/dsa/blob/main/nonlinear/DirectedGraph.java#L161">Shortest Path with Topological Sort</a>, <a href="https://github.com/sharathone23/dsa/blob/main/nonlinear/DirectedGraph.java#L201">Dijkstra's Algorithm</a>, and <a href="https://github.com/sharathone23/dsa/blob/main/nonlinear/DirectedGraph.java#L262">Bellman-Ford Algorithm</a>. Each algorithm has unique characteristics making it suitable for specific types of graphs and applications.
 
<h2>Algorithm Comparision Table</h2>
<img src="/images/graph_shortestpath_comparision_table.png" alt="Comparision Table">
 
<h2>Conclusion</h2>
Selecting the right algorithm for finding the shortest path in a graph depends on the specific characteristics of the graph and the nature of the problem at hand. Dijkstra's and Bellman-Ford algorithms are more versatile for weighted graphs, with Bellman-Ford being unique in its ability to handle negative weights. For DAGs, the Shortest Path with Topological Sort offers an efficient solution, while BFS is ideal for unweighted graphs where the path cost is counted as the number of edges.
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This blog post is aimed at providing a quick reference and comparison of different shortest path algorithms used in graph theory and their applications in various domains.

Sharath Enugala

Algorithms - Comparing Shortest Path Algorithms in Graphs

Algorithm Comparision Table

Conclusion