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Building an optimal point-location structure in $$O(\operatorname{sort}(n))$$ I/Os. (English) Zbl 1421.68029
Summary: We revisit the problem of constructing an external memory data structure on a planar subdivision formed by $$n$$ segments to answer point location queries optimally in $$O(\log _B n)$$ I/Os. The objective is to achieve the I/O cost of $$\operatorname{sort}(n) = O(\frac{n}{B} \log _{M/B} \frac{n}{B})$$, where $$B$$ is the number of words in a disk block, and $$M$$ being the number of words in memory. The previous algorithms are able to achieve this either in expectation or under the tall cache assumption of $$M \ge B^2$$. We present the first algorithm that solves the problem deterministically for all values of $$M$$ and $$B$$ satisfying $$M \ge 2B$$.
##### MSC:
 68P05 Data structures 68U05 Computer graphics; computational geometry (digital and algorithmic aspects)
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