Direct dynamic structures for some line segment problems

Gaston H. Gonnet, J. Ian Munro, Derick Wood

Abstract: Simple direct dynamic binary tree structures for two line segment problems are introduced. Both structures provide for O(log n) updating and querying and can be based on any balanced class of binary search trees, for example, AVL trees. The measure tree solves a nondecomposable searching problem, while the stabbing tree improves the known updating and querying time for its corresponding application.