An in-place min–max priority search tree

One of the classic data structures for storing point sets in R2 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 i...

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Vydáno v:	Computational geometry : theory and applications Ročník 46; číslo 3; s. 310 - 327
Hlavní autoři:	De, Minati, Maheshwari, Anil, Nandy, Subhas C., Smid, Michiel
Médium:	Journal Article
Jazyk:	angličtina
Vydáno:	Elsevier B.V 01.04.2013
Témata:	In-place algorithm Maximum empty rectangle Min–max priority search tree Three-sided orthogonal range query In-place algorithm Min–max priority search tree Maximum empty rectangle Three-sided orthogonal range query
ISSN:	0925-7721
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Popis
Shrnutí:	One of the classic data structures for storing point sets in R2 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 R2 in O(mlogn) time with O(1) extra space, where m is the total number of maximal empty rectangles.
ISSN:	0925-7721
DOI:	10.1016/j.comgeo.2012.09.007