A general lower bound on the I/O-complexity of comparison-based algorithms

Arge, Lars; Knudsen, Mikael B.; Larsen, Kirsten

doi:10.1007/3-540-57155-8_238

Cited by 36 publications

(23 citation statements)

References 6 publications

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“…While our parameter space is constrained to a coarse grained scenario which is typical of the CGM constraints for parallel computation, we show that this parameter space is both interesting and appropriate for EM computation. Once the expression for the general lower bounds reported by [1,26,3] is specialized for the subset of the parameter space that we consider, it becomes fully compatible with our results. This answers questions of Cormen [7] and Vitter [27] on the apparent contradictions between the results of [11] and the previously stated lower bounds.…”

Section: Introductionsupporting

confidence: 54%

Reducing I/O complexity by simulating coarse grained parallel algorithms

Dehne

Hutchinson²,

Maheshwari

et al.

Proceedings 13th International Parallel Processing Symposium and 10th Symposium on Parallel and Distributed Processing. IPPS/SP

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Section: Introductionsupporting

confidence: 54%

Reducing I/O complexity by simulating coarse grained parallel algorithms

Dehne

Hutchinson²,

Maheshwari

et al.

Proceedings 13th International Parallel Processing Symposium and 10th Symposium on Parallel and Distributed Processing. IPPS/SP

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“…More recently, researchers have designed externalmemory algorithms for a number of problems in different areas, such as in computational geometry [19] and graph theoretic computation [5,14]. In [6] a general connection between the comparison-complexity and the I/O complexity of a given problem is shown, and in [4] alternative solutions for some of the problems in [14] and [19] are derived by developing and using dynamic external-memory data structures.…”

Section: Previous Results In I/o-efficient Computationmentioning

confidence: 99%

External-Memory Algorithms for Processing Line Segments in Geographic Information Systems

Arge¹,

Vengroff²,

Vitter³

1996

BRICS

Self Cite

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In the design of algorithms for large-scale applications it is essential to consider the problem of minimizing I/O communication. Geographical information systems (GIS) are good examples of such large-scale applications as they frequently handle huge amounts of spatial data. In this paper we develop efficient new external-memory algorithms for a number of important problems involving line segments in the plane, including trapezoid decomposition, batched planar point location, triangulation, red-blue line segment intersection reporting, and general line segment intersection reporting. In GIS systems, the first three problems are useful for rendering and modeling, and the latter two are frequently used for overlaying maps and extracting information from them. * An extended abstract version of this paper was presented at the Third Annual European Symposium on Algorithms (ESA '95).

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“…However, unlike our algorithm that "hides" all I/O in the buffered range tree, the algorithm is very I/O specific. That both algorithms are optimal follows from the (N log 2 N + R) comparison model lower bound and the results in [9] and [10].…”

Section: Application: Orthogonal Line Segmentmentioning

confidence: 93%

The Buffer Tree: A Technique for Designing Batched External Data Structures

Arge¹

2003

Algorithmica

135

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Abstract. We present a technique for designing external memory data structures that support batched operations I/O efficiently. We show how the technique can be used to develop external versions of a search tree, a priority queue, and a segment tree, and give examples of how these structures can be used to develop I/Oefficient algorithms. The developed algorithms are either extremely simple or straightforward generalizations of known internal memory algorithms-given the developed external data structures.Key Words. I/O efficiency, Internal memory algorithms, Batched external data structures, Buffer tree. Introduction.In recent years, increasing attention has been given to Input/Outputefficient (or I/O-efficient) algorithms. This is due to the fact that communication between fast internal memory and slower external memory such as disks is the bottleneck in many computations involving massive datasets. The significance of this bottleneck is increasing as internal computation gets faster and parallel computing gains popularity.Much work has been done on designing external versions of data structures designed for internal memory. Most of these structures are designed to be used in on-line settings, where queries should be answered immediately and within a good worst case number of I/Os. As a consequence they often do not take advantage of the available main memory, leading to suboptimal performance when they are used in solutions for batched (or offline) problems. Therefore several techniques have been developed for solving massive batched problems without using external data structures.In this paper we present a technique for designing external data structures that take advantage of the large main memory. We do so by only requiring good amortized performance and by allowing query operations to be batched. We also show how the developed data structures can be used in simple and I/O-efficient algorithms for a number of fundamental computational geometry and graph problems. Our technique has subsequently been used in the development of a large number of I/O-efficient algorithms in these and several other problem areas.

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A general lower bound on the I/O-complexity of comparison-based algorithms

Cited by 36 publications

References 6 publications

Reducing I/O complexity by simulating coarse grained parallel algorithms

Reducing I/O complexity by simulating coarse grained parallel algorithms

External-Memory Algorithms for Processing Line Segments in Geographic Information Systems

The Buffer Tree: A Technique for Designing Batched External Data Structures

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