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Optimal Finger Search Trees in the Pointer Machine
, 2002
"... We develop a new finger search tree with worst case constant update time in the Pointer Machine (PM) model of computation. This was a major problem in the field of Data Structures and was tantalizingly open for over twenty years, while many attempts by researchers were made to solve it. The result c ..."
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Cited by 10 (3 self)
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We develop a new finger search tree with worst case constant update time in the Pointer Machine (PM) model of computation. This was a major problem in the field of Data Structures and was tantalizingly open for over twenty years, while many attempts by researchers were made to solve it. The result comes as a consequence of the innovative mechanism that guides the rebalancing operations, combined with incremental multiple splitting and fusion techniques over nodes.
Persistent data structures
 IN HANDBOOK ON DATA STRUCTURES AND APPLICATIONS, CRC PRESS 2001, DINESH MEHTA AND SARTAJ SAHNI (EDITORS) BOROUJERDI, A., AND MORET, B.M.E., "PERSISTENCY IN COMPUTATIONAL GEOMETRY," PROC. 7TH CANADIAN CONF. COMP. GEOMETRY, QUEBEC
, 1995
"... ..."
Superefficient Aggregating Historyindependent Persistent Authenticated Dictionaries
"... Authenticated dictionaries allow users to send lookup requests to an untrusted server and get authenticated answers. Persistent authenticated dictionaries (PADs) add queries against historical versions. We consider a variety of different trust models for PADs and we present several extensions, incl ..."
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Cited by 6 (2 self)
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Authenticated dictionaries allow users to send lookup requests to an untrusted server and get authenticated answers. Persistent authenticated dictionaries (PADs) add queries against historical versions. We consider a variety of different trust models for PADs and we present several extensions, including support for aggregation and a rich query language, as well as hiding information about the order in which PADs were constructed. We consider variations on treelike data structures as well as a design that improves efficiency by speculative future predictions. We improve on prior constructions and feature two designs that can authenticate historical queries with constant storage per update and several designs that can return constantsized authentication results.
Dynamic Planar Range Maxima Queries
 In Proc. 38th International Colloquium on Automata, Languages, and Programming, vol 6755 of LNCS
"... Abstract. We consider the dynamic twodimensional maxima query problem. Let P be a set of n points in the plane. A point is maximal if it is not dominated by any other point in P. We describe two data structures that support the reporting of the t maximal points that dominate a given query point, an ..."
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Cited by 5 (1 self)
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Abstract. We consider the dynamic twodimensional maxima query problem. Let P be a set of n points in the plane. A point is maximal if it is not dominated by any other point in P. We describe two data structures that support the reporting of the t maximal points that dominate a given query point, and allow for insertions and deletions of points in P. In the pointer machine model we present a linear space data structure with O(log n + t) worst case query time and O(log n) worst case update time. This is the first dynamic data structure for the planar maxima dominance query problem that achieves these bounds in the worst case. The data structure also supports the more general query of reporting the maximal points among the points that lie in a given 3sided orthogonal range unbounded from above in the same complexity. We can support 4sided queries in O(log 2 n+t) worst case time, and O(log 2 n) worst case update time, using O(n log n) space, where t is the size of the output. This improves the worst case deletion time of the dynamic rectangular visibility query problem from O(log 3 n) to O(log 2 n). We adapt the data structure to the RAM model with word size w, where the coordinates of the points are integers in the range U={0,..., 2 w −1}. We present a linear space data structure that supports 3sided range maxima queries in log n log n O ( +t) worst case time and updates in O ( ) worst case time. log log n log log n These are the first sublogarithmic worst case bounds for all operations in the RAM model. 1
1 Authenticated dictionaries: Realworld costs and
, 2010
"... Authenticated dictionaries are a widely discussed paradigm to enable verifiable integrity for data storage on untrusted servers, such as today’s widely used “cloud computing ” resources, allowing a server to provide a “proof, ” typically in the form of a slice through a cryptographic data structure, ..."
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Cited by 2 (0 self)
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Authenticated dictionaries are a widely discussed paradigm to enable verifiable integrity for data storage on untrusted servers, such as today’s widely used “cloud computing ” resources, allowing a server to provide a “proof, ” typically in the form of a slice through a cryptographic data structure, that the results of any given query are the correct answer, including that the absence of a query result is correct. Persistent authenticated dictionaries (PADs) further allow queries against older versions of the structure. This research presents implementations of a variety of different PAD algorithms, some based on Merkle treestyle data structures and others based on individually signed “tuple ” statements (with and without RSA accumulators). We present system throughput benchmarks, presenting costs in terms of time, storage, and bandwidth as well as considering how much money would be required given standard cloud computing costs. We conclude that Merkle tree PADs are preferable in cases with frequent updates, while tuplebased PADs are preferable with higher query rates. For Merkle tree PADs, redblack trees outperform treaps and skiplists. Applying SarnakTarjan’s versioned node strategy, with a cache of old hashes at every node, to redblack trees yields the fastest Merkle tree PAD implementation, notably using half the memory of the more commonly used applicative path copying strategy. For tuple PADs, although we designed and implemented an algorithm using RSA accumulators that offers constant update size, constant storage per update, constant proof size, and sublinear computation per update, we found that RSA accumulators are so expensive that they are never worthwhile. We find that other optimizations in the literature for tuple PADs are more costeffective.
Exploiting the MultiAppendOnlyTrend Property of Historical Data in Data Warehouses ⋆
"... Abstract. Data warehouses maintain historical information to enable the discovery of trends and developments over time. Hence data items usually contain timerelated attributes like the time of a sales transaction or the order and shipping date of a product. Furthermore the values of these timerela ..."
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Cited by 1 (0 self)
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Abstract. Data warehouses maintain historical information to enable the discovery of trends and developments over time. Hence data items usually contain timerelated attributes like the time of a sales transaction or the order and shipping date of a product. Furthermore the values of these timerelated attributes have a tendency to increase over time. We refer to this as the MultiAppendOnlyTrend (MAOT) property. In this paper we formalize the notion of MAOT and show how taking advantage of this property can improve query performance considerably. We focus on range aggregate queries which are essential for summarizing large data sets. Compared to MOLAP data cubes the amount of precomputation and hence additional storage in the proposed technique is dramatically reduced. 1
Optimal Finger Search Trees in the Pointer Machine
"... We develop a new finger search tree with worstcase constant update time in the Pointer Machine (PM) model of computation. This was a major problem in the field of Data Structures and was tantalizingly open for over twenty years while many attempts by researchers were made to solve it. The result co ..."
Abstract
 Add to MetaCart
We develop a new finger search tree with worstcase constant update time in the Pointer Machine (PM) model of computation. This was a major problem in the field of Data Structures and was tantalizingly open for over twenty years while many attempts by researchers were made to solve it. The result comes as a consequence of the innovative mechanism that guides the rebalancing operations combined with incremental multiple splitting and fusion techniques over nodes.
Persistency in Suffix Trees with Applications to String Interval Problems
"... The suffix tree has proven to be an invaluable indexing data structure, which is widely used as a building block in many applications. We study the problem of making a suffix tree persistent. Specifically, consider a streamed text T where characters are appended to the beginning of the text. The suf ..."
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The suffix tree has proven to be an invaluable indexing data structure, which is widely used as a building block in many applications. We study the problem of making a suffix tree persistent. Specifically, consider a streamed text T where characters are appended to the beginning of the text. The suffix tree is updated for each character appended. We wish to allow access to any previous version of the suffix tree. While it is possible to support basic persistence for suffix trees using classical persistence techniques, some applications which can make use of this persistency cannot be solved efficiently using these techniques alone. A collection of such problems is that of queries on string intervals of the text indexed by the suffix tree. In other words, if the text T = t1...tn is indexed, one may want to answer different queries on string intervals, ti...tj, of the text. These types of problems are known as positionrestricted and contain querying, reporting, rank, selection etc. Persistency can be utilized to obtain solutions for these problems on prefixes of the text, by solving these problems on previous versions of the suffix tree. However, for substrings it is not sufficient to use the standard persistency. We propose more sophisticated persistent techniques which yield solutions for positionrestricted querying, reporting, rank, and selection problems. 1