Incremental hive graph
The hive graph is a rectangular graph satisfying some additional condition widely used in computational geometry for solving several kinds of fundamental queries. It has been introduced by Chazelle
In this paper we present an optimal algorithm for incrementally building a hive graph structure: while it retains the same performance in query answering, it also allows to incrementally insert new line segments with O(log n) worst case time per update. Our technique exploits a novel “eager”; approach.
Some other dynamic operations performable on our structure in optimal time, such as Purge and Backtrack, are described. Also, we discuss some applications of our results.
KeywordsLine Segment Range Query Vertical Edge Horizontal Edge Query Answering
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