Abstract
In this paper, we present techniques and algorithms for processing an offline sequence of update and query operations and for related problems. The update can be either all insertions or all deletions. The types of query include min-gap, max-gap, predecessor, and successor. Most problems we consider are solved optimally in linear time by our algorithms, which are based on new geometric modeling and interesting techniques. We also discuss some applications to which our algorithms and techniques can be applied to yield efficient solutions. These applications include an offline horizontal ray shooting problem and a shortest arc covering problem on a circle.
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