### Abstract

We present a parallel algorithm for the Voronoi diagram of the set of vertices of a convex polygon. The algorithm runs in time O(log n) and uses O(n log log n/log n) processors in the CRCW PRAM model. The concurrent write is used only by an integer sorting subroutine. We also obtain an O(log n)-time and O(n log log n/log n)-processor CRCW PRAM algorithm for the construction of the medial axis of a convex polygon. Our algorithms use the solution to the duration-unknown task scheduling problem due to Cole and Vishkin and the optimal parallel algorithm for the convex hull of a polygon due to Wagener. They are randomized in the sense that for any given l > 0 they terminate in time O(log n) with probability greater than 1 - n^{-1}.

Original language | English (US) |
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Pages (from-to) | 193-202 |

Number of pages | 10 |

Journal | Theoretical Computer Science |

Volume | 174 |

Issue number | 1-2 |

DOIs | |

State | Published - Mar 15 1997 |

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### All Science Journal Classification (ASJC) codes

- Theoretical Computer Science
- Computer Science(all)

### Cite this

*Theoretical Computer Science*,

*174*(1-2), 193-202. https://doi.org/10.1016/S0304-3975(96)00024-2

}

*Theoretical Computer Science*, vol. 174, no. 1-2, pp. 193-202. https://doi.org/10.1016/S0304-3975(96)00024-2

**A nearly optimal parallel algorithm for the Voronoi diagram of a convex polygon.** / Berman, Piotr; Lingas, Andrzej.

Research output: Contribution to journal › Article

TY - JOUR

T1 - A nearly optimal parallel algorithm for the Voronoi diagram of a convex polygon

AU - Berman, Piotr

AU - Lingas, Andrzej

PY - 1997/3/15

Y1 - 1997/3/15

N2 - We present a parallel algorithm for the Voronoi diagram of the set of vertices of a convex polygon. The algorithm runs in time O(log n) and uses O(n log log n/log n) processors in the CRCW PRAM model. The concurrent write is used only by an integer sorting subroutine. We also obtain an O(log n)-time and O(n log log n/log n)-processor CRCW PRAM algorithm for the construction of the medial axis of a convex polygon. Our algorithms use the solution to the duration-unknown task scheduling problem due to Cole and Vishkin and the optimal parallel algorithm for the convex hull of a polygon due to Wagener. They are randomized in the sense that for any given l > 0 they terminate in time O(log n) with probability greater than 1 - n-1.

AB - We present a parallel algorithm for the Voronoi diagram of the set of vertices of a convex polygon. The algorithm runs in time O(log n) and uses O(n log log n/log n) processors in the CRCW PRAM model. The concurrent write is used only by an integer sorting subroutine. We also obtain an O(log n)-time and O(n log log n/log n)-processor CRCW PRAM algorithm for the construction of the medial axis of a convex polygon. Our algorithms use the solution to the duration-unknown task scheduling problem due to Cole and Vishkin and the optimal parallel algorithm for the convex hull of a polygon due to Wagener. They are randomized in the sense that for any given l > 0 they terminate in time O(log n) with probability greater than 1 - n-1.

UR - http://www.scopus.com/inward/record.url?scp=0346675348&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0346675348&partnerID=8YFLogxK

U2 - 10.1016/S0304-3975(96)00024-2

DO - 10.1016/S0304-3975(96)00024-2

M3 - Article

VL - 174

SP - 193

EP - 202

JO - Theoretical Computer Science

JF - Theoretical Computer Science

SN - 0304-3975

IS - 1-2

ER -