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95
Selfadjusting binary search trees
, 1985
"... The splay tree, a selfadjusting form of binary search tree, is developed and analyzed. The binary search tree is a data structure for representing tables and lists so that accessing, inserting, and deleting items is easy. On an nnode splay tree, all the standard search tree operations have an am ..."
Abstract

Cited by 384 (16 self)
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The splay tree, a selfadjusting form of binary search tree, is developed and analyzed. The binary search tree is a data structure for representing tables and lists so that accessing, inserting, and deleting items is easy. On an nnode splay tree, all the standard search tree operations have an amortized time bound of O(log n) per operation, where by “amortized time ” is meant the time per operation averaged over a worstcase sequence of operations. Thus splay trees are as efficient as balanced trees when total running time is the measure of interest. In addition, for sufficiently long access sequences, splay trees are as efficient, to within a constant factor, as static optimum search trees. The efftciency of splay trees comes not from an explicit structural constraint, as with balanced trees, but from applying a simple restructuring heuristic, called splaying, whenever the tree is accessed. Extensions of splaying give simplified forms of two other data structures: lexicographic or multidimensional search trees and link/ cut trees.
Making data structures persistent
, 1989
"... This paper is a study of persistence in data structures. Ordinary data structures are ephemeral in the sense that a change to the structure destroys the old version, leaving only the new version available for use. In contrast, a persistent structure allows access to any version, old or new, at any t ..."
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Cited by 256 (5 self)
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This paper is a study of persistence in data structures. Ordinary data structures are ephemeral in the sense that a change to the structure destroys the old version, leaving only the new version available for use. In contrast, a persistent structure allows access to any version, old or new, at any time. We develop simple, systematic, and efftcient techniques for making linked data structures persistent. We use our techniques to devise persistent forms of binary search trees with logarithmic access, insertion, and deletion times and O (1) space bounds for insertion and deletion.
An asymptotically optimal multiversion Btree
, 1996
"... In a variety of applications, we need to keep track of the development of a data set over time. For maintaining and querying these multiversion data efficiently, external storage structures are an absolute necessity. We propose a multiversion Btree that supports insertions and deletions of data ite ..."
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Cited by 172 (9 self)
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In a variety of applications, we need to keep track of the development of a data set over time. For maintaining and querying these multiversion data efficiently, external storage structures are an absolute necessity. We propose a multiversion Btree that supports insertions and deletions of data items at the current version and range queries and exact match queries for any version, current or past. Our multiversion Btree is asymptotically optimal in the sense that the time and space bounds are asymptotically the same as those of the (singleversion) Btree in the worst case. The technique we present for transforming a (singleversion) Btree into a multiversion Btree is quite general: it applies to a number of hierarchical external access structures with certain properties directly, and it can be modified for others.
Planar Point Location Using Persistent Search Trees
, 1986
"... A classical problem in computational geometry is the planar point location problem. This problem calls for preprocessing a polygonal subdivision of the plane defined by n line segments so that, given a sequence of points, the polygon containing each point can be determined quickly online. Several ..."
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Cited by 171 (4 self)
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A classical problem in computational geometry is the planar point location problem. This problem calls for preprocessing a polygonal subdivision of the plane defined by n line segments so that, given a sequence of points, the polygon containing each point can be determined quickly online. Several ways of solving this problem in O(log n) query time and O(n) space are known, but they are all rather complicated. We propose a simple O(log f&querytime, O(n)space solution, using persistent search trees. A persistent search tree differs from an ordinary search tree in that after an insertion or deletion, the old version of the tree can still be accessed. We develop a persistent form of binary search tree that supports insertions and deletions in the present and queries in the past. The time per query or update is
A Locally Adaptive Data Compression Scheme
, 1986
"... A data compression scheme that exploits locality of reference, such as occurs when words are used frequently over short intervals and then fall into long periods of disuse, is described. The scheme is based on a simple heuristic for selforganizing sequential search and on variablelength encoding ..."
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Cited by 154 (2 self)
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A data compression scheme that exploits locality of reference, such as occurs when words are used frequently over short intervals and then fall into long periods of disuse, is described. The scheme is based on a simple heuristic for selforganizing sequential search and on variablelength encodings of integers. We prove that it never performs much worse than Huffman coding and can perform substantially better; experiments on real files show that its performance is usually quite close to that of Huffman coding. Our scheme has many implementation advantages: it is simple, allows fast encoding and decoding, and requires only one pass over the data to be compressed (static Huffman coding takes two passes).
Optimal Dynamic Interval Management in External Memory (Extended Abstract))
 IN PROC. IEEE SYMP. ON FOUNDATIONS OF COMP. SCI
, 1996
"... We present a space and I/Ooptimal externalmemory data structure for answering stabbing queries on a set of dynamically maintained intervals. Our data structure settles an open problem in databases and I/O algorithms by providing the first optimal externalmemory solution to the dynamic interval m ..."
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Cited by 87 (24 self)
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We present a space and I/Ooptimal externalmemory data structure for answering stabbing queries on a set of dynamically maintained intervals. Our data structure settles an open problem in databases and I/O algorithms by providing the first optimal externalmemory solution to the dynamic interval management problem, which is a special case of 2dimensional range searching and a central problem for objectoriented and temporal databases and for constraint logic programming. Our data structure simultaneously uses optimal linear space (that is, O(N/B) blocks of disk space) and achieves the optimal O(log B N + T/B) I/O query bound and O(log B N ) I/O update bound, where B is the I/O block size and T the number of elements in the answer to a query. Our structure is also the first optimal external data structure for a 2dimensional range searching problem that has worstcase as opposed to amortized update bounds. Part of the data structure uses a novel balancing technique for efficient worstcase manipulation of balanced trees, which is of independent interest.
External Memory Data Structures
, 2001
"... In many massive dataset applications the data must be stored in space and query efficient data structures on external storage devices. Often the data needs to be changed dynamically. In this chapter we discuss recent advances in the development of provably worstcase efficient external memory dynami ..."
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Cited by 83 (37 self)
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In many massive dataset applications the data must be stored in space and query efficient data structures on external storage devices. Often the data needs to be changed dynamically. In this chapter we discuss recent advances in the development of provably worstcase efficient external memory dynamic data structures. We also briefly discuss some of the most popular external data structures used in practice.
On TwoDimensional Indexability and Optimal Range Search Indexing (Extended Abstract)
, 1999
"... Lars Arge Vasilis Samoladas y Jeffrey Scott Vitter z Abstract In this paper we settle several longstanding open problems in theory of indexability and external orthogonal range searching. In the first part of the paper, we apply the theory of indexability to the problem of twodimensional rang ..."
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Cited by 81 (28 self)
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Lars Arge Vasilis Samoladas y Jeffrey Scott Vitter z Abstract In this paper we settle several longstanding open problems in theory of indexability and external orthogonal range searching. In the first part of the paper, we apply the theory of indexability to the problem of twodimensional range searching. We show that the special case of 3sided querying can be solved with constant redundancy and access overhead. From this, we derive indexing schemes for general 4sided range queries that exhibit an optimal tradeoff between redundancy and access overhead.