Name
Abstract | ||
|---|---|---|
The Rubik's Cube is perhaps the world's most famous and iconic puzzle, well-known to have a rich underlying mathematical structure (group theory). In this paper, we show that the Rubik's Cube also has a rich underlying algorithmic structure. Specifically, we show that the n×n×n Rubik's Cube, as well as the n×n× 1 variant, has a "God's Number" (diameter of the configuration space) of Θ(n2/ log n). The upper bound comes from effectively parallelizing standard Θ(n2) solution algorithms, while the lower bound follows from a counting argument. The upper bound gives an asymptotically optimal algorithm for solving a general Rubik's Cube in the worst case. Given a specific starting state, we show how to find the shortest solution in an n×O(1)×O(1) Rubik's Cube. Finally, we show that finding this optimal solution becomes NP-hard in an n×n× 1 Rubik's Cube when the positions and colors of some cubies are ignored (not used in determining whether the cube is solved). |
Year | DOI | Venue |
|---|---|---|
2011 | 10.1007/978-3-642-23719-5_58 | ESA'11 Proceedings of the 19th European conference on Algorithms |
Keywords | DocType | Volume |
n rubik,optimal solution,general rubik,asymptotically optimal algorithm,shortest solution,solution algorithm,configuration space,log n,rich underlying mathematical structure,rich underlying algorithmic structure | Conference | abs/1106.5736 |
ISSN | Citations | PageRank |
0302-9743 | 5 | 1.01 |
References | Authors | |
8 | 5 | |
Name | Order | Citations | PageRank |
|---|---|---|---|
| Erik D. Demaine | 1 | 4624 | 388.59 |
| Martin L. Demaine | 2 | 592 | 84.37 |
| Sarah Eisenstat | 3 | 53 | 7.88 |
| Anna Lubiw | 4 | 753 | 95.36 |
| Andrew Winslow | 5 | 91 | 15.29 |