Shortest paths on polyhedral surfaces

2005 ◽  
pp. 243-254 ◽  
Author(s):  
Joseph O'Rourke ◽  
Subhash Suri ◽  
Heather Booth
Keyword(s):  
Shortest Paths ◽  
Polyhedral Surfaces

Finding the Shortest Path on a Polyhedral Surface and Its Application to Quality Assurance of Electric Components

2004 ◽  
Vol 126 (6) ◽  
pp. 1017-1026 ◽  
Author(s):  
Masaru Kageura ◽  
Kenji Shimada
Keyword(s):  
Product Design ◽  
Shortest Path ◽  
Shortest Paths ◽  
Computational Cost ◽  
Computational Method ◽  
Polyhedral Surface ◽  
Global Optimality ◽  
Shortest Path Algorithm ◽  
Suzuki Method ◽  
Polyhedral Surfaces

This paper presents a computational method for finding the shortest path along polyhedral surfaces. This method is useful for verifying that there is a sufficient distance between two electrical components to prevent the occurrence of a spark between them in product design. We propose an extended algorithm based on the Kanai-Suzuki method, which finds an approximate shortest path by reducing the problem to searching the shortest path on the discrete weighted graph that corresponds to a polyhedral surface. The accuracy of the solution obtained by the Kanai-Suzuki method is occasionally insufficient for our requirements in product design. To achieve higher accuracy without increasing the computational cost drastically, we extend the algorithm by adopting two additional methods: “geometrical improvement” and the “K shortest path algorithm.” Geometrical improvement improves the local optimality by using the geometrical information around a path obtained by the graph method. The K shortest path algorithm, on the other hand, improves the global optimality by finding multiple initial paths for searching the shortest path. For some representative polyhedral surfaces we performed numerical experiments and demonstrated the effectiveness of the proposed method by comparing the shortest paths obtained by the Chen-Han exact method and the Kanai-Suzuki approximate method with the ones obtained by our method.

Determining approximate shortest paths on weighted polyhedral surfaces

2005 ◽  
Vol 52 (1) ◽  
pp. 25-53 ◽  
Author(s):  
L. Aleksandrov ◽  
A. Maheshwari ◽  
J.-R. Sack
Keyword(s):  
Shortest Paths ◽  
Polyhedral Surfaces

Exact Geodesics and Shortest Paths on Polyhedral Surfaces

2009 ◽  
Vol 31 (6) ◽  
pp. 1006-1016 ◽  
Author(s):  
M. Balasubramanian ◽  
J.R. Polimeni ◽  
E.L. Schwartz
Keyword(s):  
Shortest Paths ◽  
Polyhedral Surfaces

Approximating Shortest Paths on Weighted Polyhedral Surfaces

Algorithmica ◽  
2001 ◽  
Vol 30 (4) ◽  
pp. 527-562 ◽  
Author(s):  
M. Lanthier ◽  
A. Maheshwari ◽  
J. -R. Sack
Keyword(s):  
Shortest Paths ◽  
Polyhedral Surfaces

eMap: A Web Application for Identifying and Visualizing Electron or Hole Hopping Pathways in Proteins

2019 ◽  
Author(s):  
Ruslan N. Tazhigulov ◽  
James R. Gayvert ◽  
Melissa Wei ◽  
Ksenia B. Bravaya
Keyword(s):  
Web Application ◽  
Shortest Paths ◽  
Coarse Grained ◽  
Decay Parameter ◽  
Electron Hole ◽  
Web Based ◽  
Aromatic Amino Acid Residue ◽  
Pathways Model ◽  
Visualization Tools ◽  
Effective Decay

<p>eMap is a web-based platform for identifying and visualizing electron or hole transfer pathways in proteins based on their crystal structures. The underlying model can be viewed as a coarse-grained version of the Pathways model, where each tunneling step between hopping sites represented by electron transfer active (ETA) moieties is described with one effective decay parameter that describes protein-mediated tunneling. ETA moieties include aromatic amino acid residue side chains and aromatic fragments of cofactors that are automatically detected, and, in addition, electron/hole residing sites that can be specified by the users. The software searches for the shortest paths connecting the user-specified electron/hole source to either all surface-exposed ETA residues or to the user-specified target. The identified pathways are ranked based on their length. The pathways are visualized in 2D as a graph, in which each node represents an ETA site, and in 3D using available protein visualization tools. Here, we present the capability and user interface of eMap 1.0, which is available at https://emap.bu.edu.</p>

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.

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