Experiments on the Practical I/o Eeciency of Geometric Algorithms: Distribution Sweep vs. Plane Sweep Experiments on the Practical I/o Eeciency of Geometric Algorithms: Distribution Sweep vs. Plane Sweep

We present an extensive experimental study comparing the performance of four algorithms for the following orthogonal segment intersection problem: given a set of horizontal and vertical line segments in the plane, report all intersecting horizontal-vertical pairs. The problem has important applications in VLSI layout and graphics, which are large-scale in nature. The algorithms under evaluation are distribution sweep and three variations of plane sweep. Distribution sweep is speciically designed for the situations in which the problem is too large to be solved in internal memory, and theoretically has optimal I/O cost. Plane sweep is a well-known and powerful technique in computational geometry, and is optimal for this particular problem in terms of internal computation. The three variations of plane sweep diier by the sorting methods (external vs. internal sorting) used in the preprocessing phase and the dynamic data structures (B tree vs. 2-3-4 tree) used in the sweeping phase. We generate the test data by three programs that use a random number generator while producing some interesting properties that are predicted by our theoretical analysis. The sizes of the test data range from 250 thousand segments to 2.5 million segments. The experiments provide detailed quantitative evaluation of the performance of the four algorithms, and the observed behavior of the algorithms is consistent with their theoretical properties. This is the rst experimental work comparing the practical performance between external-memory algorithms and conventional algorithms with large-scale test data.