Λεπτομέρειες βιβλιογραφικής εγγραφής
| Τίτλος: |
Deterministic protocols for Voronoi diagrams and triangulations of planar point sets on the congested clique |
| Συγγραφείς: |
Jansson, Jesper, Levcopoulos, Christos, Lingas, Andrzej, Polishchuk, Valentin, Xue, Quan |
| Συνεισφορές: |
Lund University, Faculty of Engineering, LTH, Departments at LTH, Department of Computer Science, Lunds universitet, Lunds Tekniska Högskola, Institutioner vid LTH, Institutionen för datavetenskap, Originator |
| Πηγή: |
Theoretical Computer Science. 1055 |
| Θεματικοί όροι: |
Natural Sciences, Computer and Information Sciences, Computer Sciences, Naturvetenskap, Data- och informationsvetenskap (Datateknik), Datavetenskap (Datalogi) |
| Περιγραφή: |
We study the problems of computing the Voronoi diagram and a triangulation of a set of n2 points with O(logn)-bit coordinates in the Euclidean plane in a substantially sublinear in n number of rounds in the congested clique model with n nodes. First, we observe that if the points are uniformly at random distributed in a unit square then their Voronoi diagram within the square can be computed in O(1) rounds with high probability (w.h.p.). Next, we show that if a very weak smoothness condition is satisfied by an input set of n2 points with O(logn)-bit coordinates in the unit square then the Voronoi diagram of the point set within the unit square can be deterministically computed in O(logn) rounds in this model. Finally, we present a deterministic O(logn)-round protocol for a triangulation of n2 points with O(logn)-bit coordinates in the Euclidean plane. It relies on our novel method for extending triangulations of two planar point sets separated by a straight line to a complete triangulation of the union of the sets in O(1) rounds. |
| Σύνδεσμος πρόσβασης: |
https://doi.org/10.1016/j.tcs.2025.115491 |
| Βάση Δεδομένων: |
SwePub |