# Parallel Geometric Algorithms in Coarse-Grain Network Models

## Abstract

We present efficient deterministic parallel algorithmic techniques for solving geometric problems in BSP like coarse-grain network models. Our coarse-grain network techniques seek to achieve scalability and minimization of both the communication time and local computation time. These techniques enable us to solve a number of geometric problems in the plane, such as computing the visibility of non-intersecting line segments, computing the convex hull, visibility, and dominating maxima of a simple polygon, two-variable linear programming, determination of the monotonicity of a simple polygon, computing the kernel of a simple polygon, etc. Our coarse-grain algorithms represent theoretical improvement over previously known results, and take into consideration additional practical features of coarse-grain network computation.

## Keywords

Simple Polygon Geometric Problem Communication Round Internal Segment Vertical Region## Preview

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