Semi-dynamic shortest paths and breadth-first search in digraphs

1997 ◽  
pp. 33-46 ◽  
Author(s):  
Paolo Giulio Franciosa ◽  
Daniele Frigioni ◽  
Roberto Giaccio
Keyword(s):  
Shortest Paths ◽  
Breadth First Search ◽  
Dynamic Shortest Paths

Computer algorithms

2018 ◽  
Author(s):  
Mark Newman
Keyword(s):  
Data Structures ◽  
Analysis Of Algorithms ◽  
Shortest Paths ◽  
Minimum Cut ◽  
Network Data ◽  
Computer Algorithms ◽  
Breadth First Search ◽  
Augmenting Path ◽  
Basic Concepts ◽  
Maximum Flows

This chapter introduces some of the fundamental concepts of numerical network calculations. The chapter starts with a discussion of basic concepts of computational complexity and data structures for storing network data, then progresses to the description and analysis of algorithms for a range of network calculations: breadth-first search and its use for calculating shortest paths, shortest distances, components, closeness, and betweenness; Dijkstra's algorithm for shortest paths and distances on weighted networks; and the augmenting path algorithm for calculating maximum flows, minimum cut sets, and independent paths in networks.

Indoor landmark-based path-finding utilising the expanded connectivity of an endpoint partition

2016 ◽  
Vol 45 (2) ◽  
pp. 233-252
Author(s):  
Pepijn Viaene ◽  
Alain De Wulf ◽  
Philippe De Maeyer
Keyword(s):  
Visual Information ◽  
Spatial Configuration ◽  
Shortest Paths ◽  
Minimal Amount ◽  
Path Finding ◽  
Breadth First Search ◽  
Length Increase ◽  
Efficient Communication ◽  
Indoor Wayfinding

Landmarks are ideal wayfinding tools to guide a person from A to B as they allow fast reasoning and efficient communication. However, very few path-finding algorithms start from the availability of landmarks to generate a path. In this paper, which focuses on indoor wayfinding, a landmark-based path-finding algorithm is presented in which the endpoint partition is proposed as spatial model of the environment. In this model, the indoor environment is divided into convex sub-shapes, called e-spaces, that are stable with respect to the visual information provided by a person’s surroundings (e.g. walls, landmarks). The algorithm itself implements a breadth-first search on a graph in which mutually visible e-spaces suited for wayfinding are connected. The results of a case study, in which the calculated paths were compared with their corresponding shortest paths, show that the proposed algorithm is a valuable alternative for Dijkstra’s shortest path algorithm. It is able to calculate a path with a minimal amount of actions that are linked to landmarks, while the path length increase is comparable to the increase observed when applying other path algorithms that adhere to natural wayfinding behaviour. However, the practicability of the proposed algorithm is highly dependent on the availability of landmarks and on the spatial configuration of the building.

scholarly journals The Number of Moves of the Largest Disc in Shortest Paths on Hanoi Graphs

10.37236/4252 ◽  
2014 ◽  
Vol 21 (4) ◽  
Author(s):  
Simon Aumann ◽  
Katharina A.M. Götz ◽  
Andreas M. Hinz ◽  
Ciril Petr
Keyword(s):  
Shortest Paths ◽  
General Setting ◽  
Optimal Number ◽  
Numerical Results ◽  
Breadth First Search ◽  
Tower Of Hanoi ◽  
Optimal Paths ◽  
Widespread Interest ◽  
Binary Strings

In contrast to the widespread interest in the Frame-Stewart conjecture (FSC) about the optimal number of moves in the classical Tower of Hanoi task with more than three pegs, this is the first study of the question of investigating shortest paths in Hanoi graphs $H_p^n$ in a more general setting. Here $p$ stands for the number of pegs and $n$ for the number of discs in the Tower of Hanoi interpretation of these graphs. The analysis depends crucially on the number of largest disc moves (LDMs). The patterns of these LDMs will be coded as binary strings of length $p-1$ assigned to each pair of starting and goal states individually. This will be approached both analytically and numerically. The main theoretical achievement is the existence, at least for all $n\geqslant p(p-2)$, of optimal paths where $p-1$ LDMs are necessary. Numerical results, obtained by an algorithm based on a modified breadth-first search making use of symmetries of the graphs, lead to a couple of conjectures about some cases not covered by our ascertained results. These, in turn, may shed some light on the notoriously open FSC.

scholarly journals Improved Algorithms for Dynamic Shortest Paths

Algorithmica ◽  
2000 ◽  
Vol 28 (4) ◽  
pp. 367-389 ◽  
Author(s):  
H. N. Djidjev ◽  
G. E. Pantziou ◽  
C. D. Zaroliagis
Keyword(s):  
Shortest Paths ◽  
Dynamic Shortest Paths

scholarly journals Dynamic shortest paths minimizing travel times and costs

Networks ◽  
2003 ◽  
Vol 41 (4) ◽  
pp. 197-205 ◽  
Author(s):  
Ravindra K. Ahuja ◽  
James B. Orlin ◽  
Stefano Pallottino ◽  
Maria G. Scutellà
Keyword(s):  
Shortest Paths ◽  
Travel Times ◽  
Dynamic Shortest Paths

scholarly journals Dynamic Shortest Paths Containers

2004 ◽  
Vol 92 ◽  
pp. 65-84 ◽  
Author(s):  
Dorothea Wagner ◽  
Thomas Willhalm ◽  
Christos Zaroliagis
Keyword(s):  
Shortest Paths ◽  
Dynamic Shortest Paths

Fully dynamic shortest paths in digraphs with arbitrary arc weights

2003 ◽  
Vol 49 (1) ◽  
pp. 86-113 ◽  
Author(s):  
Daniele Frigioni ◽  
Alberto Marchetti-Spaccamela ◽  
Umberto Nanni
Keyword(s):  
Shortest Paths ◽  
Dynamic Shortest Paths
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