# Preconditioning 2D integer data for fast convex hull computations

Journal article

Cadenas, O (2016). Preconditioning 2D integer data for fast convex hull computations.

*PLoS ONE.*11 (3).

Authors | Cadenas, O |
---|---|

Abstract | In order to accelerate computing the convex hull on a set of n points, a heuristic procedure is often applied to reduce the number of points to a set of s points, s ≤n, which also contains the same hull. We present an algorithm to precondition 2D data with integer coordinates bounded by a box of size p × q before building a 2D convex hull, with three distinct advantages. First, we prove that under the condition min(p, q) ≤ n the algorithm executes in time within O(n); second, no explicit sorting of data is required; and third, the reduced set of s points forms a simple polygonal chain and thus can be directly pipelined into an O(n) time convex hull algorithm. This paper empirically evaluates and quantifies the speed up gained by preconditioning a set of points by a method based on the proposed algorithm before using common convex hull algorithms to build the final hull. A speedup factor of at least four is consistently found from experiments on various datasets when the condition min(p, q) n ≤holds; the smaller the ratio min(p, q)/n is in the dataset, the greater the speedup factor achieved. |

Keywords | Computing Convex Hull; 2D Integer data; Preconditioning data; MD Multidisciplinary; General Science & Technology |

Year | 2016 |

Journal | PLoS ONE |

Journal citation | 11 (3) |

Publisher | Public Library of Science (PLoS) |

ISSN | 1932-6203 |

Digital Object Identifier (DOI) | doi:10.1371/journal.pone.0149860 |

Publication dates | |

Print | 03 Mar 2016 |

Publication process dates | |

Deposited | 08 May 2017 |

Accepted | 22 Feb 2016 |

Publisher's version | License CC BY 4.0 |

https://openresearch.lsbu.ac.uk/item/874xz

##### 1

total views##### 24

total downloads##### 1

views this month##### 3

downloads this month

## Related outputs

##### Preprocessing 2D data for fast convex hull computations

Cadenas, O and Megson, GM (2019). Preprocessing 2D data for fast convex hull computations.*PLoS ONE.*14 (2), p. e0212189.

##### Running Median Algorithm and Implementation for Integer Streaming Applications

Cadenas, O and Megson, GM (2018). Running Median Algorithm and Implementation for Integer Streaming Applications.*IEEE Embedded Systems Letters.*

##### KurSL: Model of anharmonic coupled oscillations based on Kuramoto coupling and Sturm-Liouville problem

Cadenas, O, Laszuk, D and Slawomir, N (2018). KurSL: Model of anharmonic coupled oscillations based on Kuramoto coupling and Sturm-Liouville problem.*Advances in Data Science and Adaptive Analysis.*10 (02).

##### Rapid preconditioning of data for accelerating convex hull algorithms

Cadenas, O and Megson, G (2014). Rapid preconditioning of data for accelerating convex hull algorithms.*Electronics Letters.*50 (4), pp. 270-272.

##### Virtualization for cost-effective teaching of assembly language

Cadenas, O, Sherratt, S, Howlett, D, Guy, C and Lundqvist, K (2015). Virtualization for cost-effective teaching of assembly language.*IEEE Transactions on Education.*58 (4), pp. 282-288.

##### Median architecture by accumulative parallel counters

Cadenas, O, Megson, G and Sherratt, S (2015). Median architecture by accumulative parallel counters.*IEEE Transactions on Circuits and Systems II: Express Briefs.*62 (7), pp. 661-665.

##### Pipelined median architecture

Cadenas, O (2015). Pipelined median architecture.*Electronics Letters.*51 (24), pp. 1999-2001.

##### EMD performance comparison: single vs double floating points

Laszuk, D, Cadenas, O. and Nasuto, J (2016). EMD performance comparison: single vs double floating points.*International journal of signal processing systems.*4 (4), pp. 349-353.

##### On the Phase Coupling of Two Components Mixing in Empirical Mode Decomposition

Laszuk, D, Cadenas, O. and Nasuto, Slawomir J. (2016). On the Phase Coupling of Two Components Mixing in Empirical Mode Decomposition.*Advances in Data Science and Adaptive Analysis.*8 (1).