Building an Optimal Point-Location Structure in O( sort (n)) I/Os

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(n/Blog _M/Bn/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 ≥ B^2 . We present the first algorithm that solves the problem deterministically for all values of M and B satisfying M ≥ 2B .