Improvement of the greedy algorithm for (n2 - 1)-puzzle Online publication date: Fri, 15-Sep-2017
by Kaede Utsunomiya; Yuichi Asahiro
International Journal of Innovative Computing and Applications (IJICA), Vol. 8, No. 3, 2017
Abstract: The (n2 - 1)-puzzle is a generalisation of the well-known 15-puzzle. Ratner and Warmuth (1990) showed that finding a shortest sequence of moves for the (n2 - 1)-puzzle is NP-hard. Many researches have been devoted to the (n2 - 1)-puzzle so far. Also, the (n2 - 1)-puzzle is chosen as a benchmark problem in many researches developing a new method/strategy. For the (n2 - 1)-puzzle, a real-time algorithm is proposed by Parberry (1995), which is based on a greedy method and completes the puzzle in at most 5n3 - 9n2 / 2 + O(n) moves and needs O(1) computation time per move, although there is no guarantee that the number of moves is optimal (shortest). Following the direction of the research by Parberry (1995), we present an algorithm, which is designed by modifying Parberry's algorithm and giving a tight analysis. The number of moves by the new algorithm is smaller, which needs at most 5n3 - 11n2 + O(n) moves, and computation time per move is also O(1).
Existing subscribers:
Go to Inderscience Online Journals to access the Full Text of this article.
If you are not a subscriber and you just want to read the full contents of this article, buy online access here.Complimentary Subscribers, Editors or Members of the Editorial Board of the International Journal of Innovative Computing and Applications (IJICA):
Login with your Inderscience username and password:
Want to subscribe?
A subscription gives you complete access to all articles in the current issue, as well as to all articles in the previous three years (where applicable). See our Orders page to subscribe.
If you still need assistance, please email subs@inderscience.com
Our Blog 
Follow us on Twitter 
Visit us on Facebook