On the design of a constructive algorithm to solve the multi-peg towers of Hanoi problem

The multi-peg Towers of Hanoi problem is still open. No provably optimal constructive algorithm to solve the problem is known. The minimum number of moves required is also unknown. This paper analyses the properties of an optimal algorithm and presents a deterministic algorithm to solve the problem....

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Bibliographic Details
Published in:Theoretical computer science Vol. 237; no. 1; pp. 407 - 421
Main Author: Sarkar, U.K.
Format: Journal Article
Language:English
Published: Amsterdam Elsevier B.V 28.04.2000
Elsevier
Subjects:
Applied sciences
Combinatorial explosion
Combinatorial problem
Design of algorithm
Dynamic programming
Exact sciences and technology
Game theory
Operational research and scientific management
Operational research. Management science
Recursive formulation
Towers of Hanoi
Combinatorial explosion
Recursive formulation
Dynamic programming
Towers of Hanoi
Design of algorithm
Combinatorial problem
Multiple peg towers of Hanoi problem
Optimal solution
Hanoi tower
Game theory
Complexity
ISSN:0304-3975, 1879-2294
Online Access:Get full text
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Summary:The multi-peg Towers of Hanoi problem is still open. No provably optimal constructive algorithm to solve the problem is known. The minimum number of moves required is also unknown. This paper analyses the properties of an optimal algorithm and presents a deterministic algorithm to solve the problem. An execution trace of the algorithm is given. An important conjecture called the serialization conjecture is presented. The proposed algorithm is proved to be optimal subject to the validity of the conjecture.
ISSN:0304-3975
1879-2294
DOI:10.1016/S0304-3975(00)00020-7