eng
Schloss Dagstuhl – Leibniz-Zentrum für Informatik
Leibniz International Proceedings in Informatics
1868-8969
2018-12-06
47:1
47:13
10.4230/LIPIcs.ISAAC.2018.47
article
Streaming Algorithms for Planar Convex Hulls
Farach-Colton, Martín
1
Li, Meng
1
Tsai, Meng-Tsung
2
Department of Computer Science, Rutgers University, Piscataway, USA
Department of Computer Science, National Chiao Tung University, Hsinchu, Taiwan
Many classical algorithms are known for computing the convex hull of a set of n point in R^2 using O(n) space. For large point sets, whose size exceeds the size of the working space, these algorithms cannot be directly used. The current best streaming algorithm for computing the convex hull is computationally expensive, because it needs to solve a set of linear programs.
In this paper, we propose simpler and faster streaming and W-stream algorithms for computing the convex hull. Our streaming algorithm has small pass complexity, which is roughly a square root of the current best bound, and it is simpler in the sense that our algorithm mainly relies on computing the convex hulls of smaller point sets. Our W-stream algorithms, one of which is deterministic and the other of which is randomized, have nearly-optimal tradeoff between the pass complexity and space usage, as we established by a new unconditional lower bound.
https://drops.dagstuhl.de/storage/00lipics/lipics-vol123-isaac2018/LIPIcs.ISAAC.2018.47/LIPIcs.ISAAC.2018.47.pdf
Convex Hulls
Streaming Algorithms
Lower Bounds