Abstract. The Tower of Hanoi problem is generalized by placing pegs on the vertices of a given di... more Abstract. The Tower of Hanoi problem is generalized by placing pegs on the vertices of a given directed graph G with two distinguished vertices, S and D, and allowing moves only along arcs of this graph. An optimal solution for such a graph G is an algorithm that completes the task of moving a tower of any given number of disks from S to D in a minimal number of disk moves. In this article we present an algorithm which solves the problem for two infinite families of graphs, and prove its optimality. To the best of our knowledge, this is the first optimality proof for an infinite family of graphs. Furthermore, we present a unified algorithm that solves the problem for a wider family of graphs and conjecture its optimality.
The Tower of Hanoi problem is generalized in such a way that the pegs are located at the vertices... more The Tower of Hanoi problem is generalized in such a way that the pegs are located at the vertices of a directed graph G, and moves of disks may be made only along edges of G. Leiss obtained a complete characterization of graphs in which arbitrarily many disks can be moved from the source vertex S to the destination vertex D. Here we consider graphs which do not satisfy this characterization; hence, there is a bound on the number of disks which can be handled. Denote by g n the maximal such number as G varies over all such graphs with n vertices and S, D vary over the vertices.
The Tower of Hanoi problem is generalized by placing pegs on the vertices of a given directed gra... more The Tower of Hanoi problem is generalized by placing pegs on the vertices of a given directed graph G with two distinguished vertices, S and D, and allowing moves only along arcs of this graph. An optimal solution for such a graph G is an algorithm that completes the task of moving a tower of any given number of disks from S to D in a minimal number of disk moves.
Abstract. The Tower of Hanoi problem is generalized by placing pegs on the vertices of a given di... more Abstract. The Tower of Hanoi problem is generalized by placing pegs on the vertices of a given directed graph G with two distinguished vertices, S and D, and allowing moves only along arcs of this graph. An optimal solution for such a graph G is an algorithm that completes the task of moving a tower of any given number of disks from S to D in a minimal number of disk moves. In this article we present an algorithm which solves the problem for two infinite families of graphs, and prove its optimality. To the best of our knowledge, this is the first optimality proof for an infinite family of graphs. Furthermore, we present a unified algorithm that solves the problem for a wider family of graphs and conjecture its optimality.
The Tower of Hanoi problem is generalized in such a way that the pegs are located at the vertices... more The Tower of Hanoi problem is generalized in such a way that the pegs are located at the vertices of a directed graph G, and moves of disks may be made only along edges of G. Leiss obtained a complete characterization of graphs in which arbitrarily many disks can be moved from the source vertex S to the destination vertex D. Here we consider graphs which do not satisfy this characterization; hence, there is a bound on the number of disks which can be handled. Denote by g n the maximal such number as G varies over all such graphs with n vertices and S, D vary over the vertices.
The Tower of Hanoi problem is generalized by placing pegs on the vertices of a given directed gra... more The Tower of Hanoi problem is generalized by placing pegs on the vertices of a given directed graph G with two distinguished vertices, S and D, and allowing moves only along arcs of this graph. An optimal solution for such a graph G is an algorithm that completes the task of moving a tower of any given number of disks from S to D in a minimal number of disk moves.
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Papers by Dany Azriel