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58
External Memory Algorithms and Data Structures
, 1998
"... Data sets in large applications are often too massive to fit completely inside the computer's internal memory. The resulting input/output communication (or I/O) between fast internal memory and slower external memory (such as disks) can be a major performance bottleneck. In this paper, we survey the ..."
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Cited by 320 (24 self)
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Data sets in large applications are often too massive to fit completely inside the computer's internal memory. The resulting input/output communication (or I/O) between fast internal memory and slower external memory (such as disks) can be a major performance bottleneck. In this paper, we survey the state of the art in the design and analysis of external memory algorithms and data structures (which are sometimes referred to as "EM" or "I/O" or "outofcore" algorithms and data structures). EM algorithms and data structures are often designed and analyzed using the parallel disk model (PDM). The three machineindependent measures of performance in PDM are the number of I/O operations, the CPU time, and the amount of disk space. PDM allows for multiple disks (or disk arrays) and parallel CPUs, and it can be generalized to handle tertiary storage and hierarchical memory. We discuss several important paradigms for how to solve batched and online problems efficiently in external memory. Programming tools and environments are available for simplifying the programming task. The TPIE system (Transparent Parallel I/O programming Environment) is both easy to use and efficient in terms of execution speed. We report on some experiments using TPIE in the domain of spatial databases. The newly developed EM algorithms and data structures that incorporate the paradigms we discuss are significantly faster than methods currently used in practice.
On Indexing Mobile Objects
, 1999
"... We show how to index mobile objects in one and two dimensions using efficient dynamic external memory data structures. The problem is motivated by real life applications in traffic monitoring, intelligent navigation and mobile communications domains. For the 1dimensional case, we give (i) a dynamic ..."
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Cited by 200 (14 self)
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We show how to index mobile objects in one and two dimensions using efficient dynamic external memory data structures. The problem is motivated by real life applications in traffic monitoring, intelligent navigation and mobile communications domains. For the 1dimensional case, we give (i) a dynamic, external memory algorithm with guaranteed worst case performance and linear space and (ii) a practical approximation algorithm also in the dynamic, external memory setting, which has linear space and expected logarithmic query time. We also give an algorithm with guaranteed logarithmic query time for a restricted version of the problem. We present extensions of our techniques to two dimensions. In addition we give a lower bound on the number of I/O's needed to answer the ddimensional problem. Initial experimental results and comparisons to traditional indexing approaches are also included. 1 Introduction Traditional database management systems assume that data stored in the database rem...
Indexing moving points
, 2003
"... We propose three indexing schemes for storing a set S of N points in the plane, each moving along a linear trajectory, so that any query of the following form can be answered quickly: Given a rectangle R and a real value t; report all K points of S that lie inside R at time t: We first present an in ..."
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Cited by 168 (13 self)
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We propose three indexing schemes for storing a set S of N points in the plane, each moving along a linear trajectory, so that any query of the following form can be answered quickly: Given a rectangle R and a real value t; report all K points of S that lie inside R at time t: We first present an indexing structure that, for any given constant e> 0; uses OðN=BÞ disk blocks and answers a query in OððN=BÞ 1=2þe þ K=BÞ I/Os, where B is the block size. It can also report all the points of S that lie inside R during a given time interval. A point can be inserted or deleted, or the trajectory of a point can be changed, in Oðlog 2 B NÞ I/Os. Next, we present a general approach that improves the query time if the queries arrive in chronological order, by allowing the index to evolve over time. We obtain a tradeoff between the query time and the number of times the index needs to be updated as the points move. We also describe an indexing scheme in which the number of I/Os required to answer a query depends monotonically on the difference between the query time stamp t and the current time. Finally, we develop an efficient indexing scheme to answer approximate
Cacheoblivious Btrees
, 2000
"... Abstract. This paper presents two dynamic search trees attaining nearoptimal performance on any hierarchical memory. The data structures are independent of the parameters of the memory hierarchy, e.g., the number of memory levels, the blocktransfer size at each level, and the relative speeds of me ..."
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Cited by 135 (22 self)
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Abstract. This paper presents two dynamic search trees attaining nearoptimal performance on any hierarchical memory. The data structures are independent of the parameters of the memory hierarchy, e.g., the number of memory levels, the blocktransfer size at each level, and the relative speeds of memory levels. The performance is analyzed in terms of the number of memory transfers between two memory levels with an arbitrary blocktransfer size of B; this analysis can then be applied to every adjacent pair of levels in a multilevel memory hierarchy. Both search trees match the optimal search bound of Θ(1+logB+1 N) memory transfers. This bound is also achieved by the classic Btree data structure on a twolevel memory hierarchy with a known blocktransfer size B. The first search tree supports insertions and deletions in Θ(1 + logB+1 N) amortized memory transfers, which matches the Btree’s worstcase bounds. The second search tree supports scanning S consecutive elements optimally in Θ(1 + S/B) memory transfers and supports insertions and deletions in Θ(1 + logB+1 N + log2 N) amortized memory transfers, matching the performance of the Btree for B = B Ω(log N log log N).
Efficient Indexing Methods for Probabilistic Threshold Queries over Uncertain Data
 Proc. 30th Int’l Conf. Very Large Data Bases (VLDB
, 2004
"... It is infeasible for a sensor database to contain the exact value of each sensor at all points in time. This uncertainty is inherent in these systems due to measurement and sampling errors, and resource limitations. In order to avoid drawing erroneous conclusions based upon stale data, the use of un ..."
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Cited by 105 (20 self)
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It is infeasible for a sensor database to contain the exact value of each sensor at all points in time. This uncertainty is inherent in these systems due to measurement and sampling errors, and resource limitations. In order to avoid drawing erroneous conclusions based upon stale data, the use of uncertainty intervals that model each data item as a range and associated probability density function (pdf) rather than a single value has recently been proposed. Querying these uncertain data introduces imprecision into answers, in the form of probability values that specify the likeliness the answer satisfies the query. These queries are more expensive to evaluate than their traditional counterparts but are guaranteed to be correct and more informative due to the probabilities accompanying the answers. Although the answer probabilities are useful, for many applications, it is only necessary to know whether the probability exceeds a given threshold – we term these Probabilistic Threshold Queries (PTQ). In this paper we address the efficient computation of these types of queries. In particular, we develop two index structures and associated algorithms to efficiently answer PTQs. The first index scheme is based on the idea of augmenting uncertainty information to an Rtree. We establish the difficulty
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 81 (36 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 77 (27 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.
Cache Oblivious Search Trees via Binary Trees of Small Height
 In Proc. ACMSIAM Symp. on Discrete Algorithms
, 2002
"... We propose a version of cache oblivious search trees which is simpler than the previous proposal of Bender, Demaine and FarachColton and has the same complexity bounds. In particular, our data structure avoids the use of weight balanced Btrees, and can be implemented as just a single array of ..."
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Cited by 64 (9 self)
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We propose a version of cache oblivious search trees which is simpler than the previous proposal of Bender, Demaine and FarachColton and has the same complexity bounds. In particular, our data structure avoids the use of weight balanced Btrees, and can be implemented as just a single array of data elements, without the use of pointers. The structure also improves space utilization.
Two simplified algorithms for maintaining order in a list
 PROCEEDINGS OF THE 10TH ANNUAL EUROPEAN SYMPOSIUM ON ALGORITHMS (ESA
, 2002
"... In the OrderMaintenance Problem, the objective is to maintain a total order subject to insertions, deletions, and precedence queries. Known optimal solutions, due to Dietz and Sleator, are complicated. We present new algorithms that match the bounds of Dietz and Sleator. Our solutions are simple, ..."
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Cited by 62 (9 self)
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In the OrderMaintenance Problem, the objective is to maintain a total order subject to insertions, deletions, and precedence queries. Known optimal solutions, due to Dietz and Sleator, are complicated. We present new algorithms that match the bounds of Dietz and Sleator. Our solutions are simple, and we present experimental evidence that suggests that they are superior in practice.