Shortest Path Algorithms

Introduction

The shortest path problem seeks the minimum-cost path between points in a graph, where cost can represent distance, time, or any numerical metric. This problem underpins critical applications in navigation, computer networks, robotics, logistics, social network analysis, and many other fields.

Problem Definition

Given a weighted graph G = (V, E) and vertices s (source) and t (target), find the path from s to t with minimum total weight.

Types of Shortest Path Problems

Single-Source Shortest Path: From one vertex to all others
Single-Destination Shortest Path: From all vertices to one target
Single-Pair Shortest Path: Between two specific vertices
All-Pairs Shortest Path: Between every pair of vertices

Learning Path

Available Lessons

Introduction to Graphs

Fundamental Structures in Graphs

Trees and Their Applications

Graph Traversal Algorithms

Shortest Path Algorithms

Minimum Spanning Trees

Graph Connectivity and Components

Network Flow Algorithms

Shortest Path Algorithms

Key Concepts:

Shortest Path Algorithms

Lesson Sections

Shortest Path Algorithms

Introduction

Problem Definition

Types of Shortest Path Problems