On the Detection of Robust Curves

Cover On the Detection of Robust Curves
On the Detection of Robust Curves
Richard Cole
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Entation of Step 2. In pcircillrl. Stop 2 can be performed in expected O(log |A/|) time and expected 0(1^71 ■ \M\) opcration. S. We discuss Step 2. 2. The parallel implementation of Step 2. 1 is similar. The pairs of ]K)ints x and y axe processed in parallel; the result of a computation on i and y is either the line L defined by U on which x and y he or the result "no line. " These |?7|(|A/| — \l'\) results are sorted using the randomized integer sorting algorithm of Raja^ekaran and Reif [RR891.... Some Ccire is needed since this sorting algorithm tolerates inputs only from a restricted domain; e. G. , the domain of integers [1 • • • 0(|l'| ■ |Ai^|)]- This restriction is met as follows. A property of the hashing algorithm of Matias-Vishkin (and, actually of the Fredman-Komlos-Szemeredi algorithm) is that each straight line in U will be labeled by a separate integer between 1 and 5|t"|^. So, it suffices to apply the Rajasekaran-Reif sorting algorithm to these labels. Finally, the number of occurrences of each line is counted using the prefix sum algorithm of Ladner and Fischer [LFSO].

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