TY - GEN

T1 - Streaming algorithms for planar convex hulls

AU - Farach-Colton, Martín

AU - Li, Meng

AU - Tsai, Meng-Tsung

PY - 2018/12/1

Y1 - 2018/12/1

N2 - Many classical algorithms are known for computing the convex hull of a set of n point in R2 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.

AB - Many classical algorithms are known for computing the convex hull of a set of n point in R2 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.

KW - Convex Hulls

KW - Lower Bounds

KW - Streaming Algorithms

UR - http://www.scopus.com/inward/record.url?scp=85063685175&partnerID=8YFLogxK

U2 - 10.4230/LIPIcs.ISAAC.2018.47

DO - 10.4230/LIPIcs.ISAAC.2018.47

M3 - Conference contribution

AN - SCOPUS:85063685175

T3 - Leibniz International Proceedings in Informatics, LIPIcs

BT - 29th International Symposium on Algorithms and Computation, ISAAC 2018

A2 - Liao, Chung-Shou

A2 - Hsu, Wen-Lian

A2 - Lee, Der-Tsai

PB - Schloss Dagstuhl- Leibniz-Zentrum fur Informatik GmbH, Dagstuhl Publishing

Y2 - 16 December 2018 through 19 December 2018

ER -