Conference
Spanning ratio of shortest paths in weighted square tessellations
| Τίτλος: | Spanning ratio of shortest paths in weighted square tessellations |
|---|---|
| Συγγραφείς: | Bose, Prosenjit, Esteban Pascual, Guillermo, Orden Martin, David, Silveira, Rodrigo Ignacio |
| Πηγή: | UPCommons. Portal del coneixement obert de la UPC Universitat Politècnica de Catalunya (UPC) |
| Στοιχεία εκδότη: | 2022. |
| Έτος έκδοσης: | 2022 |
| Θεματικοί όροι: | Geometry, Algebraic, Graph theory, Anàlisi numèrica, Classificació AMS::65 Numerical analysis::65D Numerical approximation and computational geometry, Geometria algebraica, Classificació AMS::14 Algebraic geometry::14Q Computational aspects in algebraic geometry, Grafs, Teoria de, Àrees temàtiques de la UPC::Matemàtiques i estadística::Geometria::Geometria computacional, Classificació AMS::05 Combinatorics::05C Graph theory, Àrees temàtiques de la UPC::Matemàtiques i estadística::Geometria::Geometria algebraica, Àrees temàtiques de la UPC::Matemàtiques i estadística::Matemàtica discreta::Teoria de grafs, Numerical analysis |
| Περιγραφή: | Continuous 2-dimensional space is often discretized by considering a grid of weighted square cells. In this work we study how well a weighted tessellation approximates the space, with respect to shortest paths. In particular, we consider a shortest path SPw(s, t), which is a shortest path from s to t in the continuous weighted 2D-space, and a shortest grid path SGPw(s, t), which is a shortest path in the tessellated weighted 2D-space. Our main result is that the ratio kSGPw(s,t)k kSPw(s,t)k is at most v 2 2+v 2 ˜ 1.08, irrespective of the weight assignment. P. B. is partially supported by NSERC. G. E., D. O. and R. I. S. are partially supported by H2020-MSCA-RISE project 734922 - CONNECT and project PID2019-104129GB-I00 funded by MCIN/AEI/10.13039/501100011033. G. E. and D. O. are also supported by PIUAH21/IA-062 and CM/JIN/2021-004. G. E. is funded by an FPU of the Universidad de Alcalá. |
| Τύπος εγγράφου: | Conference object |
| Περιγραφή αρχείου: | application/pdf |
| Γλώσσα: | English |
| Σύνδεσμος πρόσβασης: | https://hdl.handle.net/2117/385087 |
| Αριθμός Καταχώρησης: | edsair.dedup.wf.002..22045f1fb75727149a55ffc0b6f1b8ee |
| Βάση Δεδομένων: | OpenAIRE |
| Η περιγραφή δεν είναι διαθέσιμη |