Christofides algorithm

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

A polynomial-time approximation algorithm for the metric traveling salesman problem with a worst-case tour-length guarantee.

The Christofides algorithm, also called the Christofides–Serdyukov algorithm, is a polynomial-time approximation method for the metric traveling salesman problem. It produces a tour guaranteed to be no more than 50% longer than the optimum, with time complexity O(n³). section 2.1.1

Use it when exact tour search becomes impractical:

• Compare approximation quality and computational cost with dynamic programming, Concorde, 2-opt, 3-opt, branch and bound, and Lin–Kernighan methods. section 2.1.1
• Apply the TSP formulation to delivery and pickup routes, school buses, service calls, meal delivery, aircraft routes, or manufacturing schedules. section 2.1.1

Figure 2.2 TSP in the Greater Toronto Area (GTA). The traveling salesman must visit all 13 cities and wishes to select the “best” path, whether that be based on distance, time, or some other criterion.

A Greater Toronto Area example frames TSP as selecting the best route through 13 cities according to distance, time, or another criterion. section 2.1.1

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

How deep it goes

States the approximation guarantee and O(n³) complexity but defers operational steps and proof details.

Examples

Uses a 13-city Greater Toronto Area route and applications including delivery, school buses, manufacturing, and service scheduling.

What you can do after

Apply it via the NetworkX package to obtain a polynomial-time approximate TSP solution.

How it connects

Connects TSP with dynamic programming, exact solvers, local search, branch and bound, metaheuristics, and learning methods.

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Related concepts

• Traveling Salesman problemaddresses · The Traveling Salesman problem is a combinatorial optimization problem that seeks a minimum-cost tour visiting each specified location exactly once and returning to the starting location.
• NetworkXused by · NetworkX is an open-source Python library for creating, manipulating, analyzing, and visualizing graphs and networks.

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.