## Combining Histograms and Parametric Curve Fitting for Feedback-Driven Query Result-Size Estimation (1999)

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Venue: | VLDB CONFERENCE |

Citations: | 31 - 1 self |

### BibTeX

@INPROCEEDINGS{König99combininghistograms,

author = {Arnd Christian König and Gerhard Weikum},

title = {Combining Histograms and Parametric Curve Fitting for Feedback-Driven Query Result-Size Estimation},

booktitle = {VLDB CONFERENCE},

year = {1999},

pages = {423--434},

publisher = {}

}

### Years of Citing Articles

### OpenURL

### Abstract

This paper aims to improve the accuracy of query result-size estimations in query optimizers by leveraging the dynamic feedback obtained from observations on the executed query workload. To this end, an approximate "synopsis" of data-value distributions is devised that combines histograms with parametric curve fitting, leading to a specific class of linear splines. The approach reconciles the benefits of histograms, simplicity and versatility, with those of parametric techniques especially the adaptivity to statistically biased and dynamically evolving query workloads. The paper

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Citation Context ...n accuracy and practicability is made by MaxDi (V,A) histograms [24] orV-optimal using Sort Parameters other than Frequency [17] . Histograms can be e ciently constructed by sampling-based techniques =-=[25, 10]-=-. Another promising approach are Wavelet-based histograms [21], which so far have only been examined in the context of range queries, however. Parametric Techniques. Parametric techniques (also known ... |

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Citation Context ...4] orV-optimal using Sort Parameters other than Frequency [17] . Histograms can be e ciently constructed by sampling-based techniques [25, 10]. Another promising approach are Wavelet-based histograms =-=[21]-=-, which so far have only been examined in the context of range queries, however. Parametric Techniques. Parametric techniques (also known as curve- tting or regression techniques) approximate value di... |

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Citation Context .... However, since the sampling itself is typically carried out at the time of the approximation, the resulting overhead prohibits the use of sampling for query optimization. Therefore, in recent works =-=[10, 8]-=- techniques for incremental maintenance of random samples have been developed.sSince our main concern is a compact representation of data, and not its acquisition, we will now concentrate on the prope... |

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Citation Context ...ively static representation in that they do not easily adapt themselves to dynamically evolving value distributions (the only exceptional work being the methods for incrementalshistograms proposed by =-=[10], whi-=-ch, however, need to maintain a \backing sample" in addition to the histogram itself and are thus not exactly light-weight either). Furthermore, a histogram is a statistically unbiased representa... |

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Citation Context ... in a bucket, which is impractical in real systems. A good compromise between accuracy and practicability is made by MaxDi (V,A) histograms [24] orV-optimal using Sort Parameters other than Frequency =-=[17]-=- . Histograms can be e ciently constructed by sampling-based techniques [25, 10]. Another promising approach are Wavelet-based histograms [21], which so far have only been examined in the context of r... |

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Citation Context ... our knowledge, have so far been restricted to parametric techniques. 3 Architectural Assumptions and Notation 3.1 Feedback-driven Architecture Following the earlier proposals by [4] and, especially, =-=[18]-=- for adaptive selectivity estimation and dynamic re-optimization of query execution plans, we assume that the database system monitors the sizes (i.e., cardinalities in the sense of bags) of intermedi... |

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Citation Context ...ult sizes for the query at hand (for survey material see [20, 1, 24, 2]). From a generalized perspective, all these approaches can be viewed as constructing an approximate representation, or synopsis =-=[11, 9]-=-, of the data for the purpose of estimation (or even giving approximative query answers, which isnot considered in this paper, however). With modern OLAP tools and other forms of decision-support quer... |

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Citation Context ...iderable overhead when \ tting" long series of query feedbacks. However, since the feedback arrives incrementally, we can use an iterative tting technique know astherecursive least squares regres=-=sion [29]-=-. For this incremental approach, we only need to maintain two m m matrices, as opposed to a k m matrix. These matrices are updated with each feedback (for a detailed description of recursive least squ... |

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Citation Context ...Oracle, Microsoft SQL Server, Sybase and Teradata. The histogram accuracy depends on the type of histogram used: While V-optimal(F,F) histograms have been proven optimal for equi-joins and selections =-=[15, 13, 16]-=-, they require a list of all attribute values in a bucket, which is impractical in real systems. A good compromise between accuracy and practicability is made by MaxDi (V,A) histograms [24] orV-optima... |

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Citation Context ...s initially, and m upon termination), and executes 4 different types of operations: 1. Removing an item from the priority queue Q. We use an implementation of priority queues based on Fibonacci heaps =-=[22]-=-, allowing the removal of an item in a queue of size n in O(log 2 n) time. 2. Merging two buckets, requiring constant time. 3. Calculating the error resulting from a merge, requiring constant time. 4.... |

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Citation Context ...ore accurate estimations for frequently queried values or value ranges. Sampling. These techniques compute their estimates by collecting and processing random samples of the data. Sampling techniques =-=[12, 3, 7, 19]-=- offer high accuracy and probabilistic guarantees on the quality of the estimation. However, since the sampling itself is typically carried out at the time of the approximation, the resulting overhead... |

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Citation Context ...error E 0 = spline err [lowl,1;highl,1) + P m i=l spline err [low 0 i ;hig0 hi) <E. Because of this property, the problem of nding an optimal partitioning can be seen as a dynamic programming problem =-=[27]-=-. This allows us to formulate a recursive rede nition of formula 6: De ne opt errlow;m := the optimal overall error for tting [vlow;vn) by m buckets. err [low;high) := the approximation error spline e... |

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Citation Context ...ribution, this provides an accurate and compact approximation; however, since the shape of the distribution is usually not known beforehand, this is often not the case. To overcome this in exibility, =-=[28, 4]-=- use a general polynomial function and apply least-squares tting to choose its coe cients. [4] additionally uses query feedback; hereby, the approximation is able to adapt to changes in the value dist... |

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Citation Context ...ult sizes for the query at hand (for survey material see [20, 1, 24, 2]). From a generalized perspective, all these approaches can be viewed as constructing an approximate representation, or synopsis =-=[11, 9]-=-, of the data for the purpose of estimation (or even giving approximative query answers, which isnot considered in this paper, however). With modern OLAP tools and other forms of decision-support quer... |

21 |
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Citation Context ... our knowledge, have so far been restricted to parametric techniques. 3 Architectural Assumptions and Notation 3.1 Feedback-driven Architecture Following the earlier proposals by [4] and, especially, =-=[18]-=- for adaptive selectivity estimation and dynamic re-optimization of query execution plans, we assume that the database system monitors the sizes (i.e., cardinalities in the sense of bags) of intermedi... |

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Citation Context ... attribute value and a continuous parametric representation with m buckets (m <n, and often even m n) and k parameters to be tted for each bucket, this leads to the so-called \knot placement problem&q=-=uot; [6]-=- which has been intensively studied in numerical mathematics and is known to have intractable complexity in full generality. Our restriction to linear splines and the relaxation to allow discontinuiti... |

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Citation Context ...ore accurate estimations for frequently queried values or value ranges. Sampling. These techniques compute their estimates by collecting and processing random samples of the data. Sampling techniques =-=[12, 3, 7, 19]-=- offer high accuracy and probabilistic guarantees on the quality of the estimation. However, since the sampling itself is typically carried out at the time of the approximation, the resulting overhead... |

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Citation Context ...ore accurate estimations for frequently queried values or value ranges. Sampling. These techniques compute their estimates by collecting and processing random samples of the data. Sampling techniques =-=[12, 3, 7, 19]-=- offer high accuracy and probabilistic guarantees on the quality of the estimation. However, since the sampling itself is typically carried out at the time of the approximation, the resulting overhead... |

1 |
Univeratility ofSerial Histograms
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(Show Context)
Citation Context ...Oracle, Microsoft SQL Server, Sybase and Teradata. The histogram accuracy depends on the type of histogram used: While V-optimal(F,F) histograms have been proven optimal for equi-joins and selections =-=[15, 13, 16]-=-, they require a list of all attribute values in a bucket, which is impractical in real systems. A good compromise between accuracy and practicability is made by MaxDi (V,A) histograms [24] orV-optima... |

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Citation Context |

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Citation Context ...ini2 tially, and m upon termination), and executes 4 different types of operations: 1. Removing an item from the priority queue Q. We use an implementation of priority queues based on Fibonacci heaps =-=[22]-=-, allowing the removal of an item in a queue of size n in O(log 2 n) time. 2. Merging two buckets, requiring constant time. 3. Calculating the error resulting from a merge, requiring constant time. 4.... |

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Citation Context ...ing (see Subsection 4.2). Using a linear function f(x) = a1 x + a0 to approximate the frequencies for the values x in a bucket leads to an improvement in accuracy, depending on the linear correlation =-=[26]-=- of the data within a bucket. P 1 high,1 First, we de ne v [low;high) := high,low l=low vl as the average attribute value within [vlow;vhigh); analogously, we de ne the average frequency f [low;high) ... |

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Citation Context ...als of a given maximum degree) , and query-specific sampling that take samples from the database to statistically estimate the intermediate result sizes for the query at hand (for survey material see =-=[20, 1, 24, 2]-=-). From a generalized perspective, all these approaches can be viewed as constructing an approximate representation, or synopsis [11, 9], of the data for the purpose of estimation (or even giving appr... |