Algorithm 64: Quicksort

Hoare, C. A. R.

doi:10.1145/366622.366644

Cited by 514 publications

(174 citation statements)

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“…In Theorem 3.1 we establish that the limiting distribution of the centred total length of the DLT is characterized by a distributional fixed-point equation, which resembles those encountered in the probabilistic analysis of algorithms such as Quicksort [7]. Such fixed-point distributional equalities, and the so-called 'divide and conquer' or recursive algorithms from which they arise, have received considerable attention recently; see, for example, [8,13,21,22].…”

Section: Introductionmentioning

confidence: 84%

On the total length of the random minimal directed spanning tree

Penrose

Wade

2006

Adv. Appl. Probab.

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In Bhatt and Roy's minimal directed spanning tree (MDST) construction for a random partially ordered set of points in the unit square, all edges must respect the "coordinatewise" partial order and there must be a directed path from each vertex to a minimal element. We study the asymptotic behaviour of the total length of this graph with power weighted edges. The limiting distribution is given by the sum of a normal component away from the boundary and a contribution introduced by the boundary effects, which can be characterized by a fixed point equation, and is reminiscent of limits arising in the probabilistic analysis of certain algorithms. As the exponent of the power weighting increases, the distribution undergoes a phase transition from the normal contribution being dominant to the boundary effects dominating. In the critical case where the weight is simple Euclidean length, both effects contribute significantly to the limit law. We also give a law of large numbers for the total weight of the graph.

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Section: Introductionmentioning

confidence: 84%

On the total length of the random minimal directed spanning tree

Penrose

Wade

2006

Adv. Appl. Probab.

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“…[25] Sideways cracking, Covered cracking [15], this paper resp. [25] Sorting: Quick(_insert) sort, Radix(_insert) [12,13] Full index: AVL-tree, B+-tree, ART [1,3,20] Parallel standard cracking P-SC [8,9] Parallel coarse-granular index P-CGI [2] Parallel-chunked standard cracking P-CSC [2] Parallel-chunked vectorized cracking P-CVC Variant of [23] Parallel-chunked coarse-granular index…”

Section: Parallel Cracking Methodsmentioning

confidence: 99%

An experimental evaluation and analysis of database cracking

Schuhknecht

Jindal²,

Dittrich

2015

The VLDB Journal

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Database cracking has been an area of active research in recent years. The core idea of database cracking is to create indexes adaptively and incrementally as a side product of query processing. Several works have proposed different cracking techniques for different aspects including updates, tuple reconstruction, convergence, concurrency control, and robustness. Our 2014 VLDB paper "The Uncracked Pieces in Database Cracking" (PVLDB 7:97-108, 2013/VLDB 2014 was the first comparative study of these different methods by an independent group. In this article, we extend our published experimental study on database cracking and bring it to an up-to-date state. Our goal is to critically review several aspects, identify the potential, and propose promising directions in database cracking. With this study, we hope to expand the scope of database cracking and possibly leverage cracking in database engines other than MonetDB. We repeat several prior database cracking works including the core cracking algorithms as well as three other works on convergence (hybrid cracking), tuple reconstruction (sideways cracking), and robustness (stochastic cracking), respectively. Additionally to our conference paper, we now also look at a recently published study about CPU efficiency (predication cracking). We evaluate these works and show possible directions to do even better. As a further extension, we evaluate the whole class of parallel cracking algorithms that were proposed in three recent works. Altogether, in this work we revisit 8 papers on database cracking and evaluate in total 18 cracking methods, 6 sorting algorithms, B Felix Martin Schuhknecht felix.schuhknecht@infosys.uni-saarland.de 1 Information Systems Group, Saarland University, Saarbrücken, Germany 2 CSAIL, MIT, Cambridge, MA, USA and 3 full index structures. Additionally, we test cracking under a variety of experimental settings, including high selectivity (Low selectivity means that many entries qualify. Consequently, a high selectivity means, that only few entries qualify) queries, low selectivity queries, varying selectivity, and multiple query access patterns. Finally, we compare cracking against different sorting algorithms as well as against different main memory optimized indexes, including the recently proposed adaptive radix tree (ART). Our results show that: (1) the previously proposed cracking algorithms are repeatable, (2) there is still enough room to significantly improve the previously proposed cracking algorithms, (3) parallelizing cracking algorithms efficiently is a hard task, (4) cracking depends heavily on query selectivity, (5) cracking needs to catch up with modern indexing trends, and (6) different indexing algorithms have different indexing signatures.

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“…Hoare's original quicksort program, as published in [7], is given as: To sort the whole array, from should be set to 0 and to should be set to |a|. The code presented above makes use of a variant partition method that does not require the caller to provide a pivot value and returns a pair rather than a single value.…”

Section: The Original Quicksortmentioning

confidence: 99%

“…To tackle this problem he invented an algorithm that was significantly faster than existing alternatives. The publication of this algorithm in 1961 as "Quicksort" [7] revolutionised the way we sort, and more generally, the way we think about and develop algorithms.…”

Section: Introductionmentioning

confidence: 99%