A Chain-Detection Algorithm for Two-Dimensional Grids

TL;DR

This paper introduces a new algorithm for detecting valid chains of pieces on two-dimensional grids, demonstrated on a chess variant, with potential applications in 3D analysis and chemistry.

Contribution

The paper presents a novel, scalable chain-detection algorithm for 2D grids, addressing a problem not fully solved by existing graph theory methods.

Findings

Algorithm successfully detects chains in SSCC positions

No incorrect results found during testing

Potential applicability to 3D and molecular chemistry

Abstract

We describe a general method of detecting valid chains or links of pieces on a two-dimensional grid. Specifically, using the example of the chess variant known as Switch-Side Chain-Chess (SSCC). Presently, no foolproof method of detecting such chains in any given chess position is known and existing graph theory, to our knowledge, is unable to fully address this problem either. We therefore propose a solution implemented and tested using the C++ programming language. We have been unable to find an incorrect result and therefore offer it as the most viable solution thus far to the chain-detection problem in this chess variant. The algorithm is also scalable, in principle, to areas beyond two-dimensional grids such as 3D analysis and molecular chemistry.