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Inplace algorithms for computing (layers of) maxima
 In: Proceedings of the 10th Scandinavian Workshop on Algorithm Theory (SWAT ’06
, 2006
"... Abstract. We describe spaceefficient algorithms for solving problems related to finding maxima among points in two and three dimensions. Our algorithms run in optimal O(n log n) time and occupy only constant extra space in addition to the space needed for representing the input. 1 ..."
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Abstract. We describe spaceefficient algorithms for solving problems related to finding maxima among points in two and three dimensions. Our algorithms run in optimal O(n log n) time and occupy only constant extra space in addition to the space needed for representing the input. 1
InPlace 2d Nearest Neighbor Search
, 2007
"... Abstract We revisit a classic problem in computational geometry: preprocessing a planar npoint set to answer nearest neighbor queries. In SoCG 2004, Br"onnimann, Chan, and Chen showed that it is possible to design an efficient data structure that takes no extra space at all other than the inpu ..."
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Abstract We revisit a classic problem in computational geometry: preprocessing a planar npoint set to answer nearest neighbor queries. In SoCG 2004, Br"onnimann, Chan, and Chen showed that it is possible to design an efficient data structure that takes no extra space at all other than the input array holding a permutation of the points. The best query time known for such "inplace data structures " is O(log 2 n). In this paper, we break the O(log 2 n) barrier by providing a method that answers nearest neighbor queries in time O((log n) log3=2 2 log log n) = O(log
InPlace Randomized Slope Selection
"... Abstract. Slope selection is a wellknown algorithmic tool used in the context of computing robust estimators for fitting a line to a collection P of n points in the plane. We demonstrate that it is possible to perform slope selection in expected O(n log n) time using only constant extra space in ad ..."
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Abstract. Slope selection is a wellknown algorithmic tool used in the context of computing robust estimators for fitting a line to a collection P of n points in the plane. We demonstrate that it is possible to perform slope selection in expected O(n log n) time using only constant extra space in addition to the space needed for representing the input. Our solution is based upon a spaceefficient variant of Matouˇsek’s randomized interpolation search, and we believe that the techniques developed in this paper will prove helpful in the design of spaceefficient randomized algorithms using samples. To underline this, we also sketch how to compute the repeated median line estimator in an inplace setting. 1
An InPlace MinMax Priority Search Tree ∗
"... 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 inplace, 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 ..."
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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 inplace, 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 answered within the same time bounds as for the original priority search tree, while using only O(1) extra space. We introduce the minmax priority search tree which is a combination of a binary search tree and a minmax 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 minmax priority search tree. As an application, we present an inplace algorithm to enumerate all maximal empty axisparallel rectangles amongst points in a rectangular region R in R 2 in O(m log n) time with O(1) extraspace, where m is the total number of maximal empty rectangles. 1