scholarly journals An ε — Approximation algorithm for weighted shortest paths on polyhedral surfaces

1998 ◽  
pp. 11-22 ◽  
Author(s):  
Lyudmil Aleksandrov ◽  
Mark Lanthier ◽  
Anil Maheshwari ◽  
Jörg -R. Sack
Keyword(s):  
Approximation Algorithm ◽  
Shortest Paths ◽  
Polyhedral Surfaces

scholarly journals An Approximation Algorithm for Computing Shortest Paths in Weighted 3-d Domains

2013 ◽  
Vol 50 (1) ◽  
pp. 124-184 ◽  
Author(s):  
Lyudmil Aleksandrov ◽  
Hristo Djidjev ◽  
Anil Maheshwari ◽  
Jörg-Rüdiger Sack
Keyword(s):  
Approximation Algorithm ◽  
Shortest Paths

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

Shortest paths on polyhedral surfaces

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

Performance Evaluation on a Hybrid Algorithm for Computing Constrained Shortest Paths

2015 ◽  
Vol 719-720 ◽  
pp. 784-790
Author(s):  
Xiang Zhu He ◽  
Gang Feng
Keyword(s):  
Approximation Algorithm ◽  
Communication Networks ◽  
Hybrid Algorithm ◽  
Shortest Paths ◽  
Service Provisioning ◽  
Fundamental Issue ◽  
Least Cost Path ◽  
Simulation Results ◽  
Quality Of Service Provisioning

Finding a delay constrained least-cost path in a directed graph is a fundamental issue for quality of service provisioning in communication networks. Recently Feng and Turkay proposed a hybrid algorithm which uses a heuristic approach to boost the average performance of a well known approximation algorithm. In this paper we provide extensive simulation results to show that the hybrid algorithm runs significantly faster than the approximation algorithm, often by one or two orders of magnitude.

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

scholarly journals Approximation Algorithm for Shortest Path in Large Social Networks

Algorithms ◽  
2020 ◽  
Vol 13 (2) ◽  
pp. 36 ◽  
Author(s):  
Dennis Nii Ayeh Mensah ◽  
Hui Gao ◽  
Liang Wei Yang
Keyword(s):  
Approximation Algorithm ◽  
Large Scale ◽  
High Efficiency ◽  
Shortest Paths ◽  
Real Life ◽  
Original Network ◽  
Hierarchical Networks ◽  
Life Data ◽  
Real Life Data ◽  
Large Scale Networks

Proposed algorithms for calculating the shortest paths such as Dijikstra and Flowd-Warshall’s algorithms are limited to small networks due to computational complexity and cost. We propose an efficient and a more accurate approximation algorithm that is applicable to large scale networks. Our algorithm iteratively constructs levels of hierarchical networks by a node condensing procedure to construct hierarchical graphs until threshold. The shortest paths between nodes in the original network are approximated by considering their corresponding shortest paths in the highest hierarchy. Experiments on real life data show that our algorithm records high efficiency and accuracy compared with other algorithms.

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