Topological Sweep in Degenerate Cases

Eynat Rafalin, Tufts University
Diane Souvaine, Tufts University
Ileana Streinu, Smith College

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Topological sweep can contribute to efficient implementations of various algorithms for data analysis. Real data, however, has degeneracies. The modification of the topological sweep algorithm presented here handles degenerate cases such as parallel or multiply concurrent lines without requiring numerical perturbations to achieve general position. Our method maintains the 0(n2) and 0(n) time and space complexities of the original algorithm, and is robust and easy to implement. We present experimental results.