# Patch-planting spin-glass solution for benchmarking

## TL;DR

This paper presents a method to generate large spin-glass instances with known solutions by stitching together smaller solved patches, enabling benchmarking of algorithms with controllable complexity.

## Contribution

The authors introduce a novel patch-planting algorithm for creating large, structured spin-glass problems with known solutions, facilitating benchmarking and complexity analysis.

## Key findings

- Patch-planting effectively creates large instances with known solutions.
- The complexity of patch-planted problems can be tuned via patch size and number.
- Patch-planted instances show different scaling behavior compared to random problems.

## Abstract

We introduce an algorithm to generate (not solve) spin-glass instances with planted solutions of arbitrary size and structure. First, a set of small problem patches with open boundaries is solved either exactly or with a heuristic, and then the individual patches are stitched together to create a large problem with a known planted solution. Because in these problems frustration is typically smaller than in random problems, we first assess the typical computational complexity of the individual patches using population annealing Monte Carlo, and introduce an approach that allows one to fine-tune the typical computational complexity of the patch-planted system. The scaling of the typical computational complexity of these planted instances with various numbers of patches and patch sizes is investigated and compared to random instances.