https://github.com/carbonicsoda/tsp-hilbert-curve-benchmark

Benchmark of Hilbert Curve Sort on the TSPLIB Dataset
https://github.com/carbonicsoda/tsp-hilbert-curve-benchmark

benchmark mathematics travelling-salesman-problem

Last synced: 8 months ago
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Benchmark of Hilbert Curve Sort on the TSPLIB Dataset

• Host: GitHub
• URL: https://github.com/carbonicsoda/tsp-hilbert-curve-benchmark
• Owner: CarbonicSoda
• Created: 2024-11-14T04:42:57.000Z (about 1 year ago)
• Default Branch: master
• Last Pushed: 2025-02-10T08:29:58.000Z (9 months ago)
• Last Synced: 2025-02-10T09:30:11.064Z (9 months ago)
• Topics: benchmark, mathematics, travelling-salesman-problem
• Language: C++
• Homepage:
• Size: 8.29 MB
• Stars: 1
• Watchers: 1
• Forks: 0
• Open Issues: 0
• Metadata Files:
  • Readme: README.md

Awesome Lists containing this project

README

          
A simple benchmark on how well the [Hilbert Curve Sort](https://github.com/CarbonicSoda/hilbert-curve-sort) performs on the TSPLIB dataset in both C++ and JS.

Particularly, the famous [pla85900.tsp](pla85900.tsp) set containing 85900 nodes.

The result is quite fascinating to me.

HilbertCurveSort2D (h2CurveSort), an algorithm that is not designed for TSP problems,

achieved a distance of 188465250 (CEIL_2D), only a rough x1.32 of the Mathematically optimal distance 142382641 (CEIL_2D).

That might seem quite bad, but many dedicated approximation algorithms do no better, yet this algorithm is more efficient.

A slight flaw of using the Hilbert Curve Sort to approximate TSP solutions, is that TSP asks for a _cycle_, not a simple tour.

Hilbert Curve Sort will not minimize the distance between the first and the last node, adding an overhead to the resultant distance,

however this is usually minor.

#### Tour Visualization

_Optimal Tour_

![Optimal Tour](assets/pla85900_optimal.png)

_Hilbert Curve Tour_

![Hilbert Curve Tour](assets/pla85900_hilbert_curve.png)

> Notice an additional horizontal line near the bottom of the tour connecting the bottom-left and the bottom-right. This is an example of the flaw I mentioned above.