liveBook · Manning

Single-source shortest path

As explained in Optimization Algorithms: AI techniques for design, planning, and control problems

The problem of finding minimum-cost paths from one source node to every other reachable node in a weighted graph.

Single-source shortest path finds minimum-cost paths from one source node to every other reachable node in a weighted graph. Dijkstra’s algorithm solves this problem when edge costs are non-negative, making it useful for routing and navigation systems. section 3.4.1

Dijkstra’s search proceeds by repeatedly selecting the closest unsettled node:

  • Place candidates in a priority queue ordered by cumulative distance from the source. section 3.4.1
  • Continue until all nodes are processed, or stop early when a required target is reached. section 3.4.1

A small graph search

Starting from S, the search first processes S, then C, D, and A in increasing cumulative-distance order. Each step revises distances and predecessors for neighboring nodes, building a shortest-path tree. section 3.4.1

How Optimization Algorithms: AI techniques for design, planning, and control problems covers it

How deep it goes
Explains initialization, priority ordering, relaxation, predecessors, and target-specific early stopping without covering implementation complexity.
Examples
Uses a toy graph with source S, nodes C, D, A, and B, plus navigation-routing applications.
What it assumes
Assumes weighted graphs, edge costs, source nodes, and graph traversal while requiring non-negative edge costs.
What you can do after
Apply Dijkstra’s algorithm to compute shortest-path distances and predecessor links from a source node.
How it connects
Connects Dijkstra’s algorithm to uniform-cost search, BFS, DFS, and bidirectional search within blind-search methods.
Cover of Optimization Algorithms: AI techniques for design, planning, and control problems
liveBookmanning.com
Read Optimization Algorithms: AI techniques for design, planning, and control problems on liveBook Get the book at manning.com

Also explained in

Compare how 2 books explain single-source shortest path →

Related concepts

This explainer was generated by Manning's knowledge graph from the text of Optimization Algorithms: AI techniques for design, planning, and control problems. The section links point to the parts of the book it draws on.