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Two- and three- dimensional point location in rectangular subdivisions
[chapter]
1992
Lecture Notes in Computer Science
We apply van Emde Boas-type stratified trees to point location problems in rectangular subdivisions in 2 and 3 dimensions. In a subdivision with n rectangles having integer coordinates from [1, U], we locate an integer query point in O«loglog U)d) query time using O(n) space when d ~ 2 or O(nloglogU) space when d = 3. Applications and extensions of this "fixed universe" approach include point location using logarithmic time an~ linear space in rectilinear subdivisions having arbitrary
doi:10.1007/3-540-55706-7_32
fatcat:4t2psyhl4fatrobscczx56cqy4