Solving a Rubik's Cube Using its Local Graph Structure

TL;DR

This paper introduces a novel heuristic based on graph convolutional networks to efficiently find the shortest solution for a scrambled Rubik's Cube by leveraging its local graph structure.

Contribution

It proposes a new heuristic, weighted convolutional distance, using graph convolutional networks to improve A* search for solving Rubik's Cubes.

Findings

The heuristic improves search efficiency for solving Rubik's Cubes.

Utilizes local graph structure to reduce computational resources.

Enhances shortest path finding in large state spaces.

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.