Solving a Rubik's Cube Using its Local Graph Structure
Abstract
The Rubix Cube is a 3-dimensional single-player combination puzzle attracting attention in the reinforcement learning community. A Rubix Cube has six faces and twelve possible actions, leading to a small and unconstrained action space and a very large state space with only one goal state. Modeling such a large state space and storing the information of each state requires exceptional computational resources, which makes it challenging to find the shortest solution to a scrambled Rubix cube with limited resources. The Rubix Cube can be represented as a graph, where states of the cube are nodes and actions are edges. Drawing on graph convolutional networks, we design a new heuristic, weighted convolutional distance, for A star search algorithm to find the solution to a scrambled Rubix Cube. This heuristic utilizes the information of neighboring nodes and convolves them with attention-like weights, which creates a deeper search for the shortest path to the solved state.
Keywords
Cite
@article{arxiv.2408.07945,
title = {Solving a Rubik's Cube Using its Local Graph Structure},
author = {Shunyu Yao and Mitchy Lee},
journal= {arXiv preprint arXiv:2408.07945},
year = {2024}
}