TY - GEN

T1 - On optimal solutions for the bottleneck tower of hanoi problem

AU - Dinitz, Yefim

AU - Solomon, Shay

PY - 2007/1/1

Y1 - 2007/1/1

N2 - We study two aspects of a generalization of the Tower of Hanoi puzzle. In 1981, D. Wood suggested its variant, where a bigger disk may be placed higher than a smaller one if their size difference is less than k. In 1992, D. Poole suggested a natural disk-moving strategy for this problem, but only in 2005, the authors proved it be optimal in the general case. We describe the family of all optimal solutions to this problem and present a closed formula for their number, as a function of the number of disks and k. Besides, we prove a tight bound for the diameter of the configuration graph of the problem suggested by Wood. Finally, we prove that the average length of shortest sequence of moves, over all pairs of initial and final configurations, is the same as the above diameter, up to a constant factor.

AB - We study two aspects of a generalization of the Tower of Hanoi puzzle. In 1981, D. Wood suggested its variant, where a bigger disk may be placed higher than a smaller one if their size difference is less than k. In 1992, D. Poole suggested a natural disk-moving strategy for this problem, but only in 2005, the authors proved it be optimal in the general case. We describe the family of all optimal solutions to this problem and present a closed formula for their number, as a function of the number of disks and k. Besides, we prove a tight bound for the diameter of the configuration graph of the problem suggested by Wood. Finally, we prove that the average length of shortest sequence of moves, over all pairs of initial and final configurations, is the same as the above diameter, up to a constant factor.

UR - http://www.scopus.com/inward/record.url?scp=38149106486&partnerID=8YFLogxK

U2 - 10.1007/978-3-540-69507-3_20

DO - 10.1007/978-3-540-69507-3_20

M3 - Conference contribution

AN - SCOPUS:38149106486

SN - 9783540695066

T3 - Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)

SP - 248

EP - 259

BT - SOFSEM 2007

PB - Springer Verlag

T2 - 33rd Conference on Current Trends in Theory and Practice of Computer Science, SOFSEM 2007

Y2 - 20 January 2007 through 26 January 2007

ER -