Building an Optimal Point-Location Structure in $$O( sort (n))$$ O ( s o r t ( n ) ) I/Os

Abstract

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 $$ sort (n) = O(\frac{n}{B} \log _{M/B} \frac{n}{B})$$ , 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 $$M \ge 2B$$ .