Toward a Dynamic Programming Solution for the 4-peg Tower of Hanoi Problem with Configurations
This work addresses a theoretical optimization problem in computer science and mathematics, but it is incremental as it builds on the existing Frame-Stewart algorithm without proving optimality or achieving broad SOTA results.
The paper tackled the 4-peg Tower of Hanoi problem by applying dynamic programming with tabling in B-Prolog to analyze disk configurations, finding that optimal partitions from the classic problem need modification for certain configurations and that random configurations may require new algorithms.
The Frame-Stewart algorithm for the 4-peg variant of the Tower of Hanoi, introduced in 1941, partitions disks into intermediate towers before moving the remaining disks to their destination. Algorithms that partition the disks have not been proven to be optimal, although they have been verified for up to 30 disks. This paper presents a dynamic programming approach to this algorithm, using tabling in B-Prolog. This study uses a variation of the problem, involving configurations of disks, in order to contrast the tabling approach with the approaches utilized by other solvers. A comparison of different partitioning locations for the Frame-Stewart algorithm indicates that, although certain partitions are optimal for the classic problem, they need to be modified for certain configurations, and that random configurations might require an entirely new algorithm.