Subquadratic Algorithms for Workload-Aware Haar Wavelet Synopses

Muthukrishnan, S.

doi:10.1007/11590156_23

Cited by 29 publications

(54 citation statements)

References 14 publications

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“…Later, in Section 5, we will show how this solution can be applied towards an equally effective solution to the dual, space-bounded problem. We focus on the problems for maximum error functions, which provide intuitive deterministic error guarantees for independent approximate values [8,9,25,35]. A maximum-error bound, as opposed to an aggregate error bound, has to be individually satisfied by each approximate value.…”

Section: Optimal Lattice Histogram Constructionmentioning

confidence: 99%

“…The gist of this analysis has appeared in [35,29,27]. In effect, the time complexity of our algorithm for space-bounded LH construction is O(n 4 log * ) with OptimalLH, and O (n + B…”

Section: Figure 8: Indirect Space-bounded Lh Constructionmentioning

confidence: 99%

“…The former, histogrambased techniques [18,21,38,37,23,22,36,11,16,14,40,12], summarize the data by dividing it into consecutive intervals, or buckets; typically, a bucket is assigned a single representative value that approximates the data therein; variations to this theme aim to optimize the data representation within a bucket [30,4,42]. The latter methods utilize a predefined hierarchical tree structure such as that defined by the Haar wavelet decomposition [32,41,5,8,9,25,35,12,13] or alternatives that follow a similar pattern [39,26,24].…”

Section: Introductionmentioning

confidence: 99%

“…Works like [23] and [16] have provided histogram construction algorithms for several error metrics, going beyond the simple heuristics of [21,38,37]. Another stream of research has attempted to provide hierarchical summarization algorithms applicable on general error metrics [8,9,25,35,13,39,27]. Still, other works have striven to define histograms in multidimensional spaces, and even build hierarchies over them at that, allowing overlaps and containment relationships between buckets [34,37,17,1,3].…”

Section: Introductionmentioning

confidence: 99%

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Optimality and scalability in lattice histogram construction

Karras

2009

Proc. VLDB Endow.

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The Lattice Histogram is a recently proposed data summarization technique that achieves approximation quality preferable to that of an optimal plain histogram. Like other hierarchical synopsis methods, a lattice histogram (LH) aims to approximate data using a hierarchical structure. Still, this structure is not defined a priori; it consists an unknown, not a given, of the problem. Past work has defined the properties that an LH needs to obey and developed general-purpose approximation algorithms for the construction thereof. Still, two major issues remain unaddressed: First, the construction of an optimal LH for a given error metric is a problem unsolved to date. Second, the proposed algorithms suffer from too high space and time complexities that render their application in real-world settings problematic. In this paper, we address both these questions, focusing on the case that the target error metric is a maximum error metric. Our algorithms treat both the error-bounded LH construction problem, in which the space occupied by an LH is minimized under an error constraint, as well as the classic space-bounded problem. First, we develop a dynamicprogramming scheme that detects an optimal LH under a given maximum-error bound. Second, we propose an efficient, practical, greedy algorithm that solves the same problem with much lower time and space requirements. Then, we show how both our algorithms can be applied to the classic space-bounded problem, aiming at minimizing error under a bound on space. Our experimental study with real-world data sets shows the effectiveness of our methods compared to competing summarization techniques. Moreover, our findings show that our greedy heuristic performs almost as well as the optimal solution in terms of accuracy.

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Section: Optimal Lattice Histogram Constructionmentioning

confidence: 99%

“…The gist of this analysis has appeared in [35,29,27]. In effect, the time complexity of our algorithm for space-bounded LH construction is O(n 4 log * ) with OptimalLH, and O (n + B…”

Section: Figure 8: Indirect Space-bounded Lh Constructionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Optimality and scalability in lattice histogram construction

Karras

2009

Proc. VLDB Endow.

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“…The second approach, such as the one taken in [3,4,14,6], is the design of algorithms that incorporate the error metric in their operation by exploiting the error tree structure. In short, due to the distributive nature of error metrics, the algorithms solve a dynamic programming recurrence, where the optimal error incurred at a node i in the error tree (for a specified space budget and for a specified set of ancestor nodes retained in the synopsis) depends on the optimal errors incurred at the two children nodes 2i, 2i+1.…”

Section: Background On Wavelet Decompositionmentioning

confidence: 99%

Constructing Optimal Wavelet Synopses

Sacharidis

2006

Current Trends in Database Technology – EDBT 2006

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Abstract. The wavelet decomposition is a proven tool for constructing concise synopses of massive data sets and rapid changing data streams, which can be used to obtain fast approximate, with accuracy guarantees, answers. In this work we present a generic formulation for the problem of constructing optimal wavelet synopses under space constraints for various error metrics, both for static and streaming data sets. We explicitly associate existing work and categorize it according to the previous problem formulation and, further, we present our current work and identify its contributions in this context. Various interesting open problems are described and our future work directions are clearly stated.

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