121 research outputs found
The Apprentices\u27 Tower of Hanoi
The Apprentices\u27 Tower of Hanoi is introduced in this thesis. Several bounds are found in regards to optimal algorithms which solve the puzzle. Graph theoretic properties of the associated state graphs are explored. A brief summary of other Tower of Hanoi variants is also presented
Graphs, Random Walks, and the Tower of Hanoi
The Tower of Hanoi puzzle with its disks and poles is familiar to students in mathematics and computing. Typically used as a classroom example of the important phenomenon of recursion, the puzzle has also been intensively studied its own right, using graph theory, probability, and other tools. The subject of this paper is “Hanoi graphs”, that is, graphs that portray all the possible arrangements of the puzzle, together with all the possible moves from one arrangement to another. These graphs are not only fascinating in their own right, but they shed considerable light on the nature of the puzzle itself. We will illustrate these graphs for different versions of the puzzle, as well as describe some important properties, such as planarity, of Hanoi graphs. Finally, we will also discuss random walks on Hanoi graphs
The number and degree distribution of spanning trees in the Tower of Hanoi graph
The number of spanning trees of a graph is an important invariant related to topological and dynamic properties of the graph, such as its reliability, communication aspects, synchronization, and so on. However, the practical enumeration of spanning trees and the study of their properties remain a challenge, particularly for large networks. In this paper, we study the number and degree distribution of the spanning trees in the Hanoi graph. We first establish recursion relations between the number of spanning trees and other spanning subgraphs of the Hanoi graph, from which we find an exact analytical expression for the number of spanning trees of the n-disc Hanoi graph. This result allows the calculation of the spanning tree entropy which is then compared with those for other graphs with the same average degree. Then, we introduce a vertex labeling which allows to find, for each vertex of the graph, its degree distribution among all possible spanning trees.Postprint (author's final draft
Covering codes in Sierpinski graphs
Graphs and AlgorithmsInternational audienceFor a graph G and integers a and b, an (a, b)-code of G is a set C of vertices such that any vertex from C has exactly a neighbors in C and any vertex not in C has exactly b neighbors in C. In this paper we classify integers a and b for which there exist (a, b)-codes in Sierpinski graphs
Planning as Tabled Logic Programming
This paper describes Picat's planner, its implementation, and planning models
for several domains used in International Planning Competition (IPC) 2014.
Picat's planner is implemented by use of tabling. During search, every state
encountered is tabled, and tabled states are used to effectively perform
resource-bounded search. In Picat, structured data can be used to avoid
enumerating all possible permutations of objects, and term sharing is used to
avoid duplication of common state data. This paper presents several modeling
techniques through the example models, ranging from designing state
representations to facilitate data sharing and symmetry breaking, encoding
actions with operations for efficient precondition checking and state updating,
to incorporating domain knowledge and heuristics. Broadly, this paper
demonstrates the effectiveness of tabled logic programming for planning, and
argues the importance of modeling despite recent significant progress in
domain-independent PDDL planners.Comment: 27 pages in TPLP 201
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