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- W4385446052 abstract "AbstractIn this paper, we present an O(n2)-time algorithm for finding the exact shortest paths from a fixed source point to all other vertices on a triangulated polyhedral surface of a polytope in three-dimensional space, where n is the number of faces of the surface. Our algorithm builds a funnel tree by level, to compute such shortest paths. The funnel tree is built by recursively splitting funnels, which are generated as described by An [Optimization, 2018]. Because their left borders are straightest geodesics, funnels are determined explicitly by the law of cosines. Known approaches such as the planar unfolding technique, source images, or projections of ones are avoided in our algorithm. Although these approaches also run in O(n2) time in the worst case, our algorithm outperforms the others in practice. Some numerical examples are presented.Keywords: Exact algorithmfunnelplanar unfoldingpolytopeshortest pathstraightest geodesictreeMathematical Subject Classifications: 05C8552B5552B5552B0568R1068W2590C59 AcknowledgmentsThe first author wishes to express his thanks to Prof. Konrad Polthier for the useful discussions and his gracious hospitality on his visits in 2017–2018 to the Institut für Mathematik, FU Berlin, where a part of this paper was written. The authors acknowledge Ho Chi Minh City University of Technology (HCMUT), VNU-HCM for supporting this study. They thank the reviewers very much for their constructive comments that helped the authors to improve greatly the paper.Disclosure statementNo potential conflict of interest was reported by the author(s).Additional informationFundingThis research is funded by Vietnam National University Ho Chi Minh City (VNU-HCM) under grant number T2022-20-01." @default.
- W4385446052 created "2023-08-02" @default.
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- W4385446052 date "2023-08-01" @default.
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- W4385446052 title "The funnel tree algorithm for finding shortest paths on polyhedral surfaces" @default.
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- W4385446052 doi "https://doi.org/10.1080/02331934.2023.2241496" @default.
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