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**1 - 4**of**4**### An efficient data structure for advance bandwidth reservation on the Internet

- University of Technology
, 1998

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### An Efficient Data Structure for Advance Bandwidth Reservationson the Internet

, 2002

"... Abstract In this contribution we present a problem of resource reservation during some time. We show that the problemhas a lower bound of \Omega (log n) per operation on average and also give a matching upper bound algorithm. ..."

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Abstract In this contribution we present a problem of resource reservation during some time. We show that the problemhas a lower bound of \Omega (log n) per operation on average and also give a matching upper bound algorithm.

### An improved algorithm for Hausdorff Voronoi diagram for non-crossing sets

, 2006

"... We present an improved algorithm for building a Hausdorff Voronoi diagram (HVD) for non-crossing objects. Our algorithm runs in O(nlog⁴ n) time, where n is the total number of points defining the objects in the plane. This improves on previous results and solves an open problem posed by Papadopoulou ..."

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We present an improved algorithm for building a Hausdorff Voronoi diagram (HVD) for non-crossing objects. Our algorithm runs in O(nlog⁴ n) time, where n is the total number of points defining the objects in the plane. This improves on previous results and solves an open problem posed by Papadopoulou and Lee [15]. Moreover, our algorithm is parallelizable. In cluster computing architectures (such as Coarse-Grained Multicomputer (CGM) [4]) our parallel algorithm for computing HVD for non-crossing objects attains speedup that is linearly proportional to the number of processors.