### Determining approximate shortest paths on weighted polyhedral surfacesDetermining approximate shortest paths on weighted polyhedral surfaces

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 Author Aleksandrov, L. ♦ Maheshwari, A. ♦ Sack, J-R Source ACM Digital Library Content type Text Publisher Association for Computing Machinery (ACM) File Format PDF Copyright Year ©2005 Language English
 Subject Domain (in DDC) Computer science, information & general works ♦ Data processing & computer science Subject Keyword Design and analysis of algorithms ♦ Approximation algorithms ♦ Computational geometry ♦ Polyhedral surfaces ♦ Shortest path problems ♦ Weighted paths Abstract In this article, we present an approximation algorithm for solving the single source shortest paths problem on weighted polyhedral surfaces. We consider a polyhedral surface $\textit{P}$ as consisting of $\textit{n}$ triangular faces, where each face has an associated positive weight. The cost of travel through a face is the Euclidean distance traveled, multiplied by the face's weight. For a given parameter ϵ, 0 <ϵ < 1, the cost of the computed paths is at most 1 + ϵ times the cost of corresponding shortest paths. Our algorithm is based on a novel way of discretizing polyhedral surfaces and utilizes a generic greedy approach for computing shortest paths in geometric graphs obtained by such discretization. Its running time is $\textit{O(C(P)}\textit{n}/&sqrt;ϵ$ log $\textit{n}/ϵ$ log 1/ϵ) time, where $\textit{C(P)}$ captures geometric parameters and the weights of the faces of $\textit{P}.$ ISSN 00045411 Age Range 18 to 22 years ♦ above 22 year Educational Use Research Education Level UG and PG Learning Resource Type Article Publisher Date 2005-01-01 Publisher Place New York e-ISSN 1557735X Journal Journal of the ACM (JACM) Volume Number 52 Issue Number 1 Page Count 29 Starting Page 25 Ending Page 53

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Source: ACM Digital Library