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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 per op ..."
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Cited by 37 (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 8 (7 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
 In Proceedings of the 15th Annual ACMSIAM Symposium on Discrete Algorithms (SODA
, 2004
"... 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 6 (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. 1
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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Cited by 2 (1 self)
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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
NEFOS: Rapid CacheAware Range Query Processing with Probabilistic Guarantees
"... Abstract. We present NEFOS (NEsted FOrest of balanced treeS), a new cacheaware indexing scheme that supports insertions and deletions in O(1) worstcase block transfers for rebalancing operations (given and update position) and searching in O(log B log n) expected block transfers, (B = disk block s ..."
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Abstract. We present NEFOS (NEsted FOrest of balanced treeS), a new cacheaware indexing scheme that supports insertions and deletions in O(1) worstcase block transfers for rebalancing operations (given and update position) and searching in O(log B log n) expected block transfers, (B = disk block size and n = number of stored elements). The expected search bound holds with high probability for any (unknown) realistic input distribution. Our expected search bound constitutes an improvement over the O(log B log n) expected bound for search achieved by the ISBtree (Interpolation Search Btree), since the latter holds with high probability for the class of smooth only input distributions. We define any unknown distribution as realistic if the smoothness doesn’t appear in the whole data set, still it may appear locally in small spatial neighborhoods. This holds for a variety of reallife nonsmooth distributions like skew, zipfian, powlaw, beta e.t.c.. The latter is also verified by an accompanying experimental study. Moreover, NEFOS is a Bparametrized concrete structure, which works for both I/O and RAM model, without any kind of transformation or adaptation. Also, it is the first time an expected sublogarithmic bound for search operation was achieved for a broad family of nonsmooth input distributions. Keywords: Data Structures, Data Management Algorithms. 1