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Line-segment intersection made in-place. (English) Zbl 1131.68113
An in-place algorithm is an algorithm which transforms a data structure using a small, constant amount of extra storage space. The input is usually overwritten by the output as the algorithm executes.
The paper deals with the problem of designing space-efficient algorithms for solving merging, sorting and partitioning problems. The author presents an in-place version of the optimal algorithm proposed by Balaban [Proceedings of the 11th Annual Symposium on Computational Geometry, ACM Press, New York, 211–219 (1995)].
The main result is the following theorem: All $$k$$ intersections induced by a set of $$n$$ segments in the plane can be computed in $$O(n\log^2(n)+k)$$ time using $$O(1)$$ very little extra words of memory.
The technique is to identify building blocks of the original algorithm and to try to replace them by in-place counterparts wherever possible.
An appendix is devoted to degenerate configurations.

##### MSC:
 68U05 Computer graphics; computational geometry (digital and algorithmic aspects) 65D18 Numerical aspects of computer graphics, image analysis, and computational geometry 68P10 Searching and sorting 68W05 Nonnumerical algorithms
heapsort
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##### References:
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