On Algorithms for Solving the Rubik's Cube

TL;DR

This paper introduces a new algorithm for solving the Rubik's cube and its variations, achieving improved move complexity and potential benefits for speedcubers.

Contribution

It presents a novel algorithm with three variations for efficiently solving the n x n x n Rubik's cube, improving move complexity from O(n^2) to O(n^2 / log n).

Findings

Algorithm always works for solving the cube.

Achieves move complexity of O(n^2 / log n).

Potential applications for speedcubers.

Abstract

In this paper, we present a novel algorithm and its three variations for solving the Rubik's cube more efficiently. This algorithm can be used to solve the complete $n \times n \times n$ cube in $O(\frac{n^2}{\log n})$ moves. This algorithm can also be useful in certain cases for speedcubers. We will prove that our algorithm always works and then perform a basic analysis on the algorithm to determine its algorithmic complexity of $O(n^2)$. Finally, we further optimize this complexity to $O(\frac{n^2}{\log n})$.