scholarly journals An Efficient Scheme for the Single Source Shortest Path Problem based on Dijkstra and SPFA Methodologies

2017 ◽  
Vol 163 (8) ◽  
pp. 46-52
Author(s):  
G.L. Prajapati ◽  
Pulkit Singhal ◽  
Ayush Ranjan ◽  
Neelesh Chourasia
Keyword(s):  
Shortest Path ◽  
Shortest Path Problem ◽  
Single Source ◽  
Efficient Scheme

Optimal Boundary Triangulations of an Interpolating Ruled Surface

2005 ◽  
Vol 5 (4) ◽  
pp. 291-301 ◽  
Author(s):  
Charlie C. L. Wang ◽  
Kai Tang
Keyword(s):  
Shortest Path ◽  
Geometric Modeling ◽  
Search Space ◽  
Shortest Path Problem ◽  
Ruled Surface ◽  
Search Problem ◽  
Combinatorial Search ◽  
Single Source ◽  
Cad Cam ◽  
Optimal Triangulation

We investigate how to define a triangulated ruled surface interpolating two polygonal directrices that will meet a variety of optimization objectives which originate from many CAD/CAM and geometric modeling applications. This optimal triangulation problem is formulated as a combinatorial search problem whose search space however has the size tightly factorial to the numbers of points on the two directrices. To tackle this bound, we introduce a novel computational tool called multilayer directed graph and establish an equivalence between the optimal triangulation and the single-source shortest path problem on the graph. Well known graph search algorithms such as the Dijkstra’s are then employed to solve the single-source shortest path problem, which effectively solves the optimal triangulation problem in O(mn) time, where n and m are the numbers of vertices on the two directrices respectively. Numerous experimental examples are provided to demonstrate the usefulness of the proposed optimal triangulation problem in a variety of engineering applications.

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