Data structures and algorithms 3: multi-dimensional searching and computational geometry
Data structures and algorithms 3: multi-dimensional searching and computational geometry
Adding range restriction capability to dynamic data structures
Journal of the ACM (JACM)
Fully dynamic point location in a monotone subdivision
SIAM Journal on Computing
Dynamic trees and dynamic point location
STOC '91 Proceedings of the twenty-third annual ACM symposium on Theory of computing
Dynamization of the trapezoid method for planar point location (extended abstract)
SCG '91 Proceedings of the seventh annual symposium on Computational geometry
Range searching in a set of line segments
SCG '85 Proceedings of the first annual symposium on Computational geometry
Biased finger trees and three-dimensional layers of maxima: (preliminary version)
SCG '94 Proceedings of the tenth annual symposium on Computational geometry
A unified approach to dynamic point location, ray shooting, and shortest paths in planar maps
SODA '93 Proceedings of the fourth annual ACM-SIAM Symposium on Discrete algorithms
Average case analysis of dynamic geometric optimization
SODA '94 Proceedings of the fifth annual ACM-SIAM symposium on Discrete algorithms
Lower bounds for dynamic transitive closure, planar point location, and parantheses matching
Nordic Journal of Computing
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The dynamic planar point location problem is the task of maintaining a dynamic set S of n non-intersecting, except possibly at endpoints, line segments in the plane under the following operations:•Locate(q point): Report the segment immediately above q, i.e., the first segment intersected by an upward vertical ray starting at q;•Insert(s segment): Add segment s to the collection S segments;•Delete(s segment): Remove segment s from the collection S of segments.We present a solution which requires space O(n), has query and insertion time O(log n loglog n) and deletion time O(log2 n). A query time below O(log2 n) was previously only known for monotone subdivisions and horizontal segments and required non-linear space.