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Patch-planting spin-glass solution for benchmarking.

Wenlong Wang¹, Salvatore Mandrà^2,3, Helmut G Katzgraber^1,4,5

¹Department of Physics and Astronomy, Texas A&M University, College Station, Texas 77843-4242, USA.

Physical Review. E

|September 28, 2017

Summary

This summary is machine-generated.

We developed a new algorithm to create complex spin-glass problems with built-in solutions. This method allows for fine-tuning computational difficulty, offering a novel way to study these challenging systems.

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Area of Science:

Computational physics
Statistical mechanics
Algorithm development

Background:

Spin-glass models are complex systems in statistical mechanics.
Generating instances with known solutions is crucial for benchmarking algorithms.
Existing methods for generating spin-glass instances have limitations.

Purpose of the Study:

To introduce a novel algorithm for generating spin-glass instances with planted solutions.
To enable the creation of instances with arbitrary size and structure.
To provide a method for fine-tuning the computational complexity of these instances.

Main Methods:

Algorithm development for generating spin-glass instances.
Solving small problem patches exactly or heuristically.
Stitching patches to form large instances with planted solutions.
Population annealing Monte Carlo for complexity assessment.
Fine-tuning computational complexity of patch-planted systems.

Main Results:

Successful generation of spin-glass instances with planted solutions.
Demonstration of fine-tuning computational complexity.
Investigation of complexity scaling with instance size and patch configuration.
Comparison of planted instance complexity to random instances.

Conclusions:

The developed algorithm offers a flexible approach to generating complex spin-glass problems.
The method allows for controlled manipulation of computational difficulty.
This work provides a valuable tool for advancing research in spin-glass systems and algorithm development.