Numerical Stability of Algorithms for Line
نویسندگان
چکیده
We analyze the behavior of two line arrangement algorithms, a sweepline algorithm and an incremental algorithm, in approximate arithmetic. The algorithms have running times O(n 2 log n) and O(n 2) respectively. We show that each of these algorithms can be implemented to have O(nn) relative error. This means that each algorithm produces an arrangement realized by a set of pseudolines so that each pseudoline diiers from the corresponding line relatively by at most O(nn). We also show that there is a line arrangement algorithm with O(n 2 log n) running time and O() relative error. 1 Introduction We analyze the behavior of line arrangement algorithms in approximate arithmetic. Approximate arithmetic is a set of arithmetic operations deened on the real numbers that
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