Min-max heaps and generalized priority queues
Communications of the ACM
Computing the largest empty rectangle
SIAM Journal on Computing
A note on finding a maximum empty rectangle
Discrete Applied Mathematics
Fast algorithms for computing the largest empty rectangle
SCG '87 Proceedings of the third annual symposium on Computational geometry
Location of the Largest Empty Rectangle among Arbitrary Obstacles
Proceedings of the 14th Conference on Foundations of Software Technology and Theoretical Computer Science
Towards in-place geometric algorithms and data structures
SCG '04 Proceedings of the twentieth annual symposium on Computational geometry
Space-efficient planar convex hull algorithms
Theoretical Computer Science - Latin American theorotical informatics
An in-place algorithm for Klee's measure problem in two dimensions
Information Processing Letters
Space-efficient geometric divide-and-conquer algorithms
Computational Geometry: Theory and Applications
Line-segment intersection made in-place
Computational Geometry: Theory and Applications
Optimal in-place and cache-oblivious algorithms for 3-d convex hulls and 2-d segment intersection
Computational Geometry: Theory and Applications
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One of the classic data structures for storing point sets in R^2 is the priority search tree, introduced by McCreight in 1985. We show that this data structure can be made in-place, i.e., it can be stored in an array such that each entry stores only one point of the point set and no entry is stored in more than one location of that array. It combines a binary search tree with a heap. We show that all the standard query operations can be performed within the same time bounds as for the original priority search tree, while using only O(1) extra space. We introduce the min-max priority search tree which is a combination of a binary search tree and a min-max heap. We show that all the standard queries which can be done in two separate versions of a priority search tree can be done with a single min-max priority search tree. As an application, we present an in-place algorithm to enumerate all maximal empty axis-parallel rectangles amongst points in a rectangular region R in R^2 in O(mlogn) time with O(1) extra space, where m is the total number of maximal empty rectangles.