A Coarse Grained Parallel Algorithm for Hausdorff Voronoi Diagrams

Authors:
Frank Dehne;Anil Maheshwari;Ryan Taylor
Affiliations:
Carleton University, Canada;Carleton University, Canada;Carleton University, Canada
Venue:
ICPP '06 Proceedings of the 2006 International Conference on Parallel Processing
Year:
2006

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Abstract

We present the first parallel algorithm for building a Hausdorff Voronoi diagram (HVD). Our algorithm is targeted towards cluster computing architectures and computes the Hausdorff Voronoi diagram for non-crossing objects in time O(n log^4 n/p ) for input size n and p processors. In addition, our parallel algorithm also implies a new sequential HVD algorithm that constructs HVDs for noncrossing objects in time O(n log^4 n). This improves on previous sequential results and solves an open problem posed by Papadopoulou and Lee [18].