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Faster Deterministic Sorting and Searching in Linear Space
, 1995
"... We present a significant improvement on linear space deterministic sorting and searching. On a unitcost RAM with word size w, an ordered set of n wbit keys (viewed as binary strings or integers) can be maintained in O ` min ` p log n; log n log w + log log n; log w log log n " time p ..."
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Cited by 38 (7 self)
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We present a significant improvement on linear space deterministic sorting and searching. On a unitcost RAM with word size w, an ordered set of n wbit keys (viewed as binary strings or integers) can be maintained in O ` min ` p log n; log n log w + log log n; log w log log n " time per operation, including insert, delete, member search, and neighbour search. The cost for searching is worstcase while the cost for updates is amortized. For range queries, there is an additional cost of reporting the found keys. As an application, n keys can be sorted in linear space at a worstcase cost of O \Gamma n p log n \Delta . The best previous method for deterministic sorting and searching in linear space has been the fusion trees which supports queries in O(logn= log log n) amortized time and sorting in O(n log n= log log n) worstcase time. We also make two minor observations on adapting our data structure to the input distribution and on the complexity of perfect hashing. 1 I...
Improved Bounds for Finger Search on a RAM
 In Algorithms – ESA 2003, LNCS Vol. 2832 (Springer 2003
, 2003
"... We present a new finger search tree with O(1) worstcase update time and O(log log d) expected search time with high probability in the Random Access Machine (RAM) model of computation for a large class of input distributions. The parameter d represents the number of elements (distance) between ..."
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Cited by 10 (9 self)
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We present a new finger search tree with O(1) worstcase update time and O(log log d) expected search time with high probability in the Random Access Machine (RAM) model of computation for a large class of input distributions. The parameter d represents the number of elements (distance) between the search element and an element pointed to by a finger, in a finger search tree that stores n elements. For the need of the analysis we model the updates by a "balls and bins" combinatorial game that is interesting in its own right as it involves insertions and deletions of balls according to an unknown distribution.
Interpolation Search for NonIndependent Data
"... We define a deterministic metric of “wellbehaved data” that enables searching along the lines of interpolation search. Specifically, define ∆ to be the ratio of distances between the farthest and nearest pair of adjacent elements. We develop a data structure that stores a dynamic set of n integers ..."
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Cited by 8 (0 self)
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We define a deterministic metric of “wellbehaved data” that enables searching along the lines of interpolation search. Specifically, define ∆ to be the ratio of distances between the farthest and nearest pair of adjacent elements. We develop a data structure that stores a dynamic set of n integers subject to insertions, deletions, and predecessor/successor queries in O(lg ∆) time per operation. This result generalizes interpolation search and interpolation search trees smoothly to nonrandom (in particular, nonindependent) input data. In this sense, we capture the amount of “pseudorandomness” required for effective interpolation search.
ISBTree: A New Indexing Scheme with Efficient Expected Behaviour. Computer Technology Institute
, 2005
"... Abstract. We present the interpolation search tree (ISBtree), a new cacheaware indexing scheme that supports update operations (insertions and deletions) in O(1) worstcase (w.c.) block transfers and search operations in O(log B log n) expected block transfers, where B represents the disk block si ..."
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Cited by 6 (5 self)
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Abstract. We present the interpolation search tree (ISBtree), a new cacheaware indexing scheme that supports update operations (insertions and deletions) in O(1) worstcase (w.c.) block transfers and search operations in O(log B log n) expected block transfers, where B represents the disk block size and n denotes the number of stored elements. The expected search bound holds with high probability for a large class of (unknown) input distributions. The w.c. search bound of our indexing scheme is O(log B n) block transfers. Our update and expected search bounds constitute a considerable improvement over the O(log B n) w.c. block transfer bounds for search and update operations achieved by the Btree and its numerous variants. This is also suggested by a set of preliminary experiments we have carried out. Our indexing scheme is based on an externalization of a main memory data structure based on interpolation search. 1
Dynamic 3sided Planar Range Queries with Expected Doubly Logarithmic Time
 Proceedings of ISAAC, 2009
"... Abstract. We consider the problem of maintaining dynamically a set of points in the plane and supporting range queries of the type [a, b] × (−∞, c]. We assume that the inserted points have their xcoordinates drawn from a class of smooth distributions, whereas the ycoordinates are arbitrarily distr ..."
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Abstract. We consider the problem of maintaining dynamically a set of points in the plane and supporting range queries of the type [a, b] × (−∞, c]. We assume that the inserted points have their xcoordinates drawn from a class of smooth distributions, whereas the ycoordinates are arbitrarily distributed. The points to be deleted are selected uniformly at random among the inserted points. For the RAM model, we present a linear space data structure that supports queries in O(log log n + t) expected time with high probability and updates in O(log log n) expected amortized time, where n is the number of points stored and t is the size of the output of the query. For the I/O model we support queries in O(log log B n + t/B) expected I/Os with high probability and updates in O(log B log n) expected amortized I/Os using linear space, where B is the disk block size. The data structures are deterministic and the expectation is with respect to the input distribution. 1
Dynamic Web Service discovery architecture based on a novel peer based overlay networks
 THE JOURNAL OF SYSTEMS AND SOFTWARE
, 2009
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Efficient Processing of 3Sided Range Queries with Probabilistic Guarantees
"... This work studies the problem of 2dimensional searching for the 3sided range query of the form [a, b] × (−∞, c] in both main and external memory, by considering a variety of input distributions. A dynamic linear main memory solution is proposed, which answers 3sided queries in O(log n + t) worst ..."
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This work studies the problem of 2dimensional searching for the 3sided range query of the form [a, b] × (−∞, c] in both main and external memory, by considering a variety of input distributions. A dynamic linear main memory solution is proposed, which answers 3sided queries in O(log n + t) worst case time and scales with O(log log n) expected with high probability update time, under continuous µrandom distributions of the x and y coordinates, where n is the current number of stored points and t is the size of the query output. Our expected update bound constitutes a considerable improvement over the O(log n) update time bound achieved by the classic Priority Search Tree of McCreight [23], as well as over the Fusion Priority log n
Dynamic Interpolation Search Revisited
"... A new dynamic Interpolation Search (IS) data structure is presented that achieves O(log log n) search time with high probability on unknown continuous or even discrete input distributions with measurable probability of key collisions, including power law and Binomial distributions. No such previou ..."
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A new dynamic Interpolation Search (IS) data structure is presented that achieves O(log log n) search time with high probability on unknown continuous or even discrete input distributions with measurable probability of key collisions, including power law and Binomial distributions. No such previous result holds for IS when the probability of key collisions is measurable. Moreover, our data structure exhibits O(1) expected search time with high probability for a wide class of input distributions that contains all those for which o(log log n) expected search time was previously known.
An Experimental Performance Comparison for Indexing Mobile Objects on the Plane ABSTRACT
"... We present a timeefficient approach to index objects moving on the plane to efficiently answer range queries about their future positions. Each object is moving with non small velocity u, meaning that the velocity value distribution is skewed (Zipf) towards umin in some range [umin,umax], where umi ..."
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We present a timeefficient approach to index objects moving on the plane to efficiently answer range queries about their future positions. Each object is moving with non small velocity u, meaning that the velocity value distribution is skewed (Zipf) towards umin in some range [umin,umax], where umin is a positive lower threshold. Our algorithm enhances a previously described solution [18] by accommodating the ISBtree access method as presented in [6]. Experimental evaluation shows the improved performance, scalability and efficiency of the new algorithm. Categories and Subject Descriptors H.2 [Database Management]: [Emergent Systems]
Technologies Research Unit
"... Web services are becoming an important enabler of the Semantic Web. Besides the need for a rich description mechanism, Web Service information should be made available in an accessible way for machine processing. In this paper, we propose a new P2P based approach for Web Services discovery. Peers th ..."
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Web services are becoming an important enabler of the Semantic Web. Besides the need for a rich description mechanism, Web Service information should be made available in an accessible way for machine processing. In this paper, we propose a new P2P based approach for Web Services discovery. Peers that store Web Services information, such as data item descriptions, are efficiently located using a scalable and robust data indexing structure for PeertoPeer data networks, NIPPERS. We present a theoretical analysis which shows that the communication cost of the query and update operations scale doublelogarithmically with the number of NIPPERS nodes. Furthermore, we show that the network is robust with respect to failures fulfilling quality of web services requirements. 1.