Related papers: Shortest paths in the Tower of Hanoi graph and fin…
The purpose of this paper is to prove the Frame-Stewart algorithm for the generalized Towers of Hanoi problem as well as finding the number of moves required to solve the problem and studying the multitude of optimal solutions. The main…
In the Twin Towers of Hanoi version of the well known Towers of Hanoi Problem there are two coupled sets of pegs. In each move, one chooses a pair of pegs in one of the sets and performs the only possible legal transfer of a disk between…
A shortest-path algorithm finds a path containing the minimal cost between two vertices in a graph. A plethora of shortest-path algorithms is studied in the literature that span across multiple disciplines. This paper presents a survey of…
The weighted Tower of Hanoi is a new generalization of the classical Tower of Hanoi problem, where a move of a disc between two pegs $i$ and $j$ is weighted by a positive real $w_{ij}\geq 0$. This new problem generalizes the concept of…
Given an undirected, weighted graph, with $n$ vertices and $m$ edges, and two special vertices $s$ and $t$, the problem is to find the shortest path between them. We give two bounded-error quantum algorithms with improved runtime in the…
Dijkstra's algorithm is the standard method for computing shortest paths on arbitrary graphs. However, it is slow for large graphs, taking at least linear time. It has been long known that for real world road networks, creating a hierarchy…
The Constraint Shortest Path (CSP) problem is as follows. An $n$-vertex graph is given, each edge/arc assigned two weights. Let us call them "cost" and "length" for definiteness. Finding a min-cost upper-bounded length path between a given…
The generalized Tower of Hanoi problem with h \ge 4 pegs is known to require a sub-exponentially fast growing number of moves in order to transfer a pile of n disks from one peg to another. In this paper we study the Path_h variant, where…
We study the reverse shortest path problem on disk graphs in the plane. In this problem we consider the proximity graph of a set of $n$ disks in the plane of arbitrary radii: In this graph two disks are connected if the distance between…
The famous Tower of Hanoi puzzle involves moving $n$ discs of distinct sizes from one of $p\geq 3$ pegs (traditionally $p=3$) to another of the pegs, subject to the constraints that only one disc may be moved at a time, and no disc can ever…
The objective of the well-known Towers of Hanoi puzzle is to move a set of disks one at a time from one of a set of pegs to another, while keeping the disks sorted on each peg. We propose an adversarial variation in which the first player…
In this paper, our aim is to prove that our recursive algorithm to solve the "Reve's puzzle" (four- peg Tower of Hanoi) is the optimal solution according to minimum number of moves. Here we used Frame's five step algorithm to solve the…
We prove the exact formulae for the expected number of moves to solve several variants of the Tower of Hanoi puzzle with 3 pegs and n disks, when each move is chosen uniformly randomly from the set of all valid moves. We further present an…
The Frame-Stewart conjecture states the least number of moves to solve a generalized Tower of Hanoi problem, of n disks and p pegs. In this paper, we prove a weaker version of the Frame-Stewart conjecture.
The determination of time-dependent collision-free shortest paths has received a fair amount of attention. Here, we study the problem of computing a time-dependent shortest path among growing discs which has been previously studied for the…
Given a graph, the shortest-path problem requires finding a sequence of edges with minimum cumulative length that connects a source vertex to a target vertex. We consider a variant of this classical problem in which the position of each…
Querying the shortest path between two vertexes is a fundamental operation in a variety of applications, which has been extensively studied over static road networks. However, in reality, the travel costs of road segments evolve over time,…
The shortest path problem in graphs is a cornerstone of AI theory and applications. Existing algorithms generally ignore edge weight computation time. We present a generalized framework for weighted directed graphs, where edge weight can be…
We investigate the problem of computing the top-$k$ simple shortest paths in weighted digraphs. While the single-pair variant -- finding the top-$k$ simple shortest paths between two specified vertices -- has been extensively studied over…
It is a critical issue to compute the shortest paths between nodes in networks. Exact algorithms for shortest paths are usually inapplicable for large scale networks due to the high computational complexity. In this paper, we propose a…