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13
An asymptotic theory for CauchyEuler differential equations with applications to the analysis of algorithms
, 2002
"... CauchyEuler differential equations surfaced naturally in a number of sorting and searching problems, notably in quicksort and binary search trees and their variations. Asymptotics of coefficients of functions satisfying such equations has been studied for several special cases in the literature. We ..."
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Cited by 22 (10 self)
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CauchyEuler differential equations surfaced naturally in a number of sorting and searching problems, notably in quicksort and binary search trees and their variations. Asymptotics of coefficients of functions satisfying such equations has been studied for several special cases in the literature. We study in this paper the most general framework for CauchyEuler equations and propose an asymptotic theory that covers almost all applications where CauchyEuler equations appear. Our approach is very general and requires almost no background on differential equations. Indeed the whole theory can be stated in terms of recurrences instead of functions. Old and new applications of the theory are given. New phase changes of limit laws of new variations of quicksort are systematically derived. We apply our theory to about a dozen of diverse examples in quicksort, binary search trees, urn models, increasing trees, etc.
Selfadjusting of ternary search tries using conditional rotations and randomized heuristics
 Comput. J
, 2005
"... A Ternary Search Trie (TST) is a highly efficient dynamic dictionary structure applicable for strings and textual data. The strings are accessed based on a set of access probabilities and are to be arranged using a TST. We consider the scenario where the probabilities are not known a priori, and is ..."
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Cited by 3 (1 self)
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A Ternary Search Trie (TST) is a highly efficient dynamic dictionary structure applicable for strings and textual data. The strings are accessed based on a set of access probabilities and are to be arranged using a TST. We consider the scenario where the probabilities are not known a priori, and is timeinvariant. Our aim is to adaptively restructure the TST so as to yield the best access or retrieval time. Unlike the case of lists and binary search trees, where numerous methods have been proposed, in the case of the TST, currently, the number of reported adaptive schemes are few. In this paper, we consider various selforganizing schemes that were applied to Binary Search Trees, and apply them to TSTs. Three new schemes, which are the splaying, the conditional rotation and the randomization heuristics, have been proposed, tested and comparatively presented. The results demonstrate that the conditional rotation heuristic is the best when compared to other heuristics that are considered in the paper.
A Dynamic Data Structure for Approximate Range Searching
, 2010
"... In this paper, we introduce a simple, randomized dynamic datastructureforstoringmultidimensionalpointsets, called a quadtreap. This data structure is a randomized, balanced variant of a quadtree data structure. In particular, it defines a hierarchical decomposition of space into cells, which are bas ..."
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Cited by 3 (2 self)
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In this paper, we introduce a simple, randomized dynamic datastructureforstoringmultidimensionalpointsets, called a quadtreap. This data structure is a randomized, balanced variant of a quadtree data structure. In particular, it defines a hierarchical decomposition of space into cells, which are based on hyperrectangles of bounded aspect ratio, each of constant combinatorial complexity. It can be viewed as a multidimensional generalization of the treap data structure of Seidel and Aragon. When inserted, points are assigned random priorities, and the tree is restructured through rotations as if the points had been inserted in priority order. In any fixed dimension d, we show it is possible to store a set of n points in a quadtreap of space O(n). The height h of the tree is O(logn) with high probability. It supports point insertion in time O(h). It supports point deletion in worstcase time O(h 2) and expectedcase time O(h), averaged over the points of the tree. It can answer εapproximate spherical range counting queries over groups and approximate nearest neighbor queries in time O ( h+ ( 1 ε)d−1).
Putting your data structure on a diet
 In preparation (2006). [Ask Jyrki for details
, 2007
"... Abstract. Consider a data structure D that stores a dynamic collection of elements. Assume that D uses a linear number of words in addition to the elements stored. In this paper several datastructural transformations are described that can be used to transform D into another data structure D ′ that ..."
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Cited by 2 (2 self)
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Abstract. Consider a data structure D that stores a dynamic collection of elements. Assume that D uses a linear number of words in addition to the elements stored. In this paper several datastructural transformations are described that can be used to transform D into another data structure D ′ that supports the same operations as D, has considerably smaller memory overhead than D, and performs the supported operations by a small constant factor or a small additive term slower than D, depending on the data structure and operation in question. The compaction technique has been successfully applied for linked lists, dictionaries, and priority queues.
Indexing for dynamic abstract regions
 Intl. Conf. on Data Engineering
, 2006
"... regions (objects) which may heavily overlap, the RCtree. These objects are “dynamic ” and may have short life spans. The novelty is that rather than representing an object by its minimum bounding rectangle (MBR), possibly with preprocessed segmentation into many small MBRs, we use the actual shape ..."
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Cited by 2 (1 self)
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regions (objects) which may heavily overlap, the RCtree. These objects are “dynamic ” and may have short life spans. The novelty is that rather than representing an object by its minimum bounding rectangle (MBR), possibly with preprocessed segmentation into many small MBRs, we use the actual shape of the object to maintain the index. This saves significant space for objects with large spatial extents since presegmentation is not needed. We show that the query performance of RCtree is much better than many indexing schemes on synthetic overlapping data sets. The performance is also competitive on reallife GIS nonoverlapping data sets. 1
Untangling binary trees via rotations
 Comput. J
"... In this paper we present a polynomial time algorithm for finding the shortest sequence of rotations that converts one binary tree into another when both binary trees are of a restricted form. The initial tree must be a degenerate tree, where every node has exactly one child, and the destination bina ..."
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Cited by 2 (0 self)
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In this paper we present a polynomial time algorithm for finding the shortest sequence of rotations that converts one binary tree into another when both binary trees are of a restricted form. The initial tree must be a degenerate tree, where every node has exactly one child, and the destination binary tree must also be degenerate, of a more restricted nature. Previous work on rotation distance has focused on approximation algorithms. Our algorithm is the only known nontrivial polynomial time algorithm for exact rotation distance between special cases of binary trees. 1.
Efficient License Validation in MPML DRM Architecture
 DRM'09
, 2009
"... Multiparty multilevel DRM architecture (MPMLDRMA) involves multiple parties such as owner, multiple levels of distributors and consumers. The owner issues redistribution licenses to its distributors, who in turn generate and issue variations of these redistribution licenses to their subdistributor ..."
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Multiparty multilevel DRM architecture (MPMLDRMA) involves multiple parties such as owner, multiple levels of distributors and consumers. The owner issues redistribution licenses to its distributors, who in turn generate and issue variations of these redistribution licenses to their subdistributors. Also the distributors generate and issue usage licenses to the consumers to consume the contents. But, these variations of the redistribution licenses and usage licenses generated and issued by each distributor must be validated by a validation authority against the redistribution licenses that it has received. In MPMLDRMA, there may exist multiple, different types of redistribution licenses for a content. Validation using multiple redistribution licenses may become difficult in real time. Further, storage of multiple redistribution licenses for validation presents a challenge of reducing storage space requirements. Hence, in this paper we propose a bitvector transform based license organizing structure, and present a method to do the validation of issued licenses in the bitvector transform domain efficiently. Experimental results show that our license organization structure helps to achieve low validation time and storage space complexity.
A Dynamic Data Structure for Approximate Range Searching
"... In this paper, we introduce a simple, randomized dynamic data structure for storing multidimensional point sets. Our particular focus is on answering approximate geometric retrieval problems, such as approximate range searching. Our data structure is essentially a partition tree, which is based on a ..."
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In this paper, we introduce a simple, randomized dynamic data structure for storing multidimensional point sets. Our particular focus is on answering approximate geometric retrieval problems, such as approximate range searching. Our data structure is essentially a partition tree, which is based on a balanced variant of the quadtree data structure. As such it has the desirable properties that it forms a hierarchical decomposition of space into cells, which are based on hyperrectangles of bounded aspect ratio, each of constant combinatorial complexity. In any fixed dimension d, we show that after O(nlogn) preprocessing, our data structure can store a set of n points in R d in space O(n) and height O(logn). It supports insertion in time O(logn) and deletion in time O(log 2 n). It also supports εapproximate spherical range (counting) queries in time O ( logn+ ( 1 ε)d−1), which is optimal for partitiontree based methods. All running times hold with high probability. Our data structure can be viewed as a multidimensional generalization of the treap data structure of Seidel and Aragon.
CAPTAIN: TAKE OFF EVERY ’ZIG’!! CAPTAIN: YOU KNOW WHAT YOU DOING. CAPTAIN: MOVE ’ZIG’. CAPTAIN: FOR GREAT JUSTICE.
"... Everything was balanced before the computers went off line. Try and adjust something, and you unbalance something else. Try and adjust that, you unbalance two more and before you know what’s happened, the ship is out of control. — Blake, Blake’s 7, “Breakdown ” (March 6, 1978) A good scapegoat is ne ..."
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Everything was balanced before the computers went off line. Try and adjust something, and you unbalance something else. Try and adjust that, you unbalance two more and before you know what’s happened, the ship is out of control. — Blake, Blake’s 7, “Breakdown ” (March 6, 1978) A good scapegoat is nearly as welcome as a solution to the problem. Let’s play.
CAPTAIN: TAKE OFF EVERY ’ZIG’!! CAPTAIN: YOU KNOW WHAT YOU DOING. CAPTAIN: MOVE ’ZIG’. CAPTAIN: FOR GREAT JUSTICE.
"... Everything was balanced before the computers went off line. Try and adjust something, and you unbalance something else. Try and adjust that, you unbalance two more and before you know what’s happened, the ship is out of control. — Blake, Blake’s 7, “Breakdown ” (March 6, 1978) A good scapegoat is ne ..."
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Everything was balanced before the computers went off line. Try and adjust something, and you unbalance something else. Try and adjust that, you unbalance two more and before you know what’s happened, the ship is out of control. — Blake, Blake’s 7, “Breakdown ” (March 6, 1978) A good scapegoat is nearly as welcome as a solution to the problem. Let’s play.