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Indexing for data models with constraints and classes
 Journal of Computer and System Sciences
, 1996
"... We examine I Oefficient data structures that provide indexing support for new data models. The database languages of these models include concepts from constraint programming (e.g., relational tuples are generated to conjunctions of constraints) and from objectoriented programming (e.g., objects a ..."
Abstract

Cited by 113 (20 self)
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We examine I Oefficient data structures that provide indexing support for new data models. The database languages of these models include concepts from constraint programming (e.g., relational tuples are generated to conjunctions of constraints) and from objectoriented programming (e.g., objects are organized in class hierarchies). Let n be the size of the database, c the number of classes, B the page size on secondary storage, and t the size of the output of a query: (1) Indexing by one attribute in many constraint data models is equivalent to external dynamic interval management, which is a special case of external dynamic twodimensional range searching. We present a semidynamic data structure for this problem that has worstcase space O(n B) pages, query I O time O(logB n+t B) and O(logB n+(logB n) 2 B) amortized insert I O time. Note that, for the static version of this problem, this is the first worstcase optimal solution. (2) Indexing by one attribute and by class name in an objectoriented model, where objects are organized
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 85 (23 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 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.
Efficient ExternalMemory Data Structures and Applications
, 1996
"... In this thesis we study the Input/Output (I/O) complexity of largescale problems arising e.g. in the areas of database systems, geographic information systems, VLSI design systems and computer graphics, and design I/Oefficient algorithms for them. A general theme in our work is to design I/Oeffic ..."
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Cited by 38 (12 self)
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In this thesis we study the Input/Output (I/O) complexity of largescale problems arising e.g. in the areas of database systems, geographic information systems, VLSI design systems and computer graphics, and design I/Oefficient algorithms for them. A general theme in our work is to design I/Oefficient algorithms through the design of I/Oefficient data structures. One of our philosophies is to try to isolate all the I/O specific parts of an algorithm in the data structures, that is, to try to design I/O algorithms from internal memory algorithms by exchanging the data structures used in internal memory with their external memory counterparts. The results in the thesis include a technique for transforming an internal memory tree data structure into an external data structure which can be used in a batched dynamic setting, that is, a setting where we for example do not require that the result of a search operation is returned immediately. Using this technique we develop batched dynamic external versions of the (onedimensional) rangetree and the segmenttree and we develop an external priority queue. Following our general philosophy we show how these structures can be used in standard internal memory sorting algorithms
Optimal External Memory Interval Management
, 2002
"... In this paper we present the external interval tree, an optimal external memory data structure for answering stabbing queries on a set of dynamically maintained intervals. The external interval tree can be used in an optimal solution to the dynamic interval management problem, which is a central pro ..."
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Cited by 32 (6 self)
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In this paper we present the external interval tree, an optimal external memory data structure for answering stabbing queries on a set of dynamically maintained intervals. The external interval tree can be used in an optimal solution to the dynamic interval management problem, which is a central problem for objectoriented and temporal databases and for constraint logic programming. Part of the structure uses a novel weightbalancing technique for efficient worstcase manipulation of balanced trees of independent interest. The external interval tree, as well at our new balancing technique, have recently been used to develop several efficient external data structures.
ExternalMemory Algorithms with Applications in Geographic Information Systems
 Algorithmic Foundations of GIS
, 1997
"... In the design of algorithms for largescale applications it is essential to consider the problem of minimizing Input/Output (I/O) communication. Geographical information systems (GIS) are good examples of such largescale applications as they frequently handle huge amounts of spatial data. In this n ..."
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Cited by 27 (9 self)
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In the design of algorithms for largescale applications it is essential to consider the problem of minimizing Input/Output (I/O) communication. Geographical information systems (GIS) are good examples of such largescale applications as they frequently handle huge amounts of spatial data. In this note we survey the recent developments in externalmemory algorithms with applications in GIS. First we discuss the AggarwalVitter I/Omodel and illustrate why normal internalmemory algorithms for even very simple problems can perform terribly in an I/Oenvironment. Then we describe the fundamental paradigms for designing I/Oefficient algorithms by using them to design efficient sorting algorithms. We then go on and survey externalmemory algorithms for computational geometry problems  with special emphasis on problems with applications in GIS  and techniques for designing such algorithms: Using the orthogonal line segment intersection problem we illustrate the distributionsweeping and ...
PBiTree coding and efficient processing of containment joins
, 2003
"... This paper addresses issues related to containment join processing in treestructured data such as XML documents. A containment join takes two sets of XML node elements as input and returns pairs of elements such that the containment relationship holds between them. While there are previous algorith ..."
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Cited by 23 (5 self)
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This paper addresses issues related to containment join processing in treestructured data such as XML documents. A containment join takes two sets of XML node elements as input and returns pairs of elements such that the containment relationship holds between them. While there are previous algorithms for processing containment joins, they require both element sets either sorted or indexed. This paper proposes a novel and complete containment query processing framework based on a new coding scheme, PBiTree code. The PBiTree code allows us to determine the ancestordescendant relationship between two elements from their PBiTreebased codes efficiently. We present algorithms in the framework that are optimized for various combinations of settings. In particular, the newly proposed partitioning based algorithms can process containment joins efficiently without sorting or indexes. Experimental results indicate that the containment join processing algorithms based on the proposed coding scheme outperform existing algorithms significantly. 1.
Binary Search Trees of Almost Optimal Height
 ACTA INFORMATICA
, 1990
"... First we present a generalization of symmetric binary Btrees, SBB(k) trees. The obtained structure has a height of only \Sigma (1 + 1k) log(n + 1)\Upsilon, where k may be chosen to be any positive integer. The maintenance algorithms require only a constant number of rotations per updating operati ..."
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Cited by 11 (1 self)
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First we present a generalization of symmetric binary Btrees, SBB(k) trees. The obtained structure has a height of only \Sigma (1 + 1k) log(n + 1)\Upsilon, where k may be chosen to be any positive integer. The maintenance algorithms require only a constant number of rotations per updating operation in the worst case. These properties together with the fact that the structure is relatively simple to implement makes it a useful alternative to other search trees in practical applications. Then, by using an SBB(k)tree with a varying k we achieve a structure with a logarithmic amortized cost per update and a height of log n + o(log n). This result is an improvement of the upper bound on the height of a dynamic binary search tree. By maintaining two trees simultaneously the amortized cost is transformed into a worstcase cost. Thus, we have improved the worstcase complexity of the dictionary problem.