How hard is it to solve a colored sliding tile puzzle?
Optimally Solving Colored Generalized Sliding-Tile Puzzles: Complexity and Bounds
October 22, 2024
https://arxiv.org/pdf/2410.14947This research paper explores the complexity of solving a type of digital puzzle involving moving colored blocks on a grid, similar to the 15-puzzle. It proves that finding the fastest solution for even simple versions of this puzzle is computationally difficult (NP-complete).
The paper's findings, particularly the analysis of movement lower bounds, could be applied to real-world LLM-based multi-agent systems where optimizing the coordinated movement of many agents (like robots in a warehouse) is crucial. The algorithms developed here, while theoretical, provide a foundation for understanding the limits of efficiency in these scenarios.