A cost model for similarity queries in metric spaces

Abstract

Wu consider tho problem of estimating CPU (distance computntlons) nnd I/O costs for processing range and k-nearest neighbors qucrics over metric spaces. Unlike the specific case of vector spaces, where information on data distribution has been exploited to derive cost models for predicting the performanco of multi-dimensional access methods, in a generic metric space there is no such a possibility, which makes the problem quite different and requires a novel approach. We insist that the distance distribution of objects can be profitably used to solve the problem, and consequently develop a concrete cost model for the M-tree access method [lo]. Our results rely on the assumption that the indexed dataset comes from a metric space which is "homogeneous" enough (in a probabilistic sense) to allow reliable cost estimations even if the distance distribution with respect to a specific query object is unknown. We experimentally validate the modol ovor both real and synthetic datasets, and show how the model can be used to tune the M-tree in order to minimlzo a combination of CPU and I/O costs. Finally, we sketch how the same approach can be applied to derive a cost model for the up-tree index structure [8].

The Basic Principles of Metric Indexing

“…11. Examples of methods that rely on this are the M-tree [77][78][79] (and its descendants), the MVP-tree [81] and D-index [50][51][52][53]101]. 12.…”

“…It is extended with a so-called exclusion zone in the Excluded Middle Vantage Point Forest [61] (which is in many ways very similar to the more recent D-index, discussed later). The BS-tree was first described by Kalantari and McDonald [45], and the BS partitioning scheme has been adopted by several subsequent structures, including the M-tree [77][78][79] and its descendants. A recent addition to the BS-tree family is the SSS-Tree [90].…”

“…For more details on the M-tree, see the papers by Zezula et al [77] and Ciaccia et al [78,79,80], for example. Some recent structures based on the M-tree include the QIC-M-tree [25], the Slim-tree [88], the DF-tree [37], the PM-tree [84], the Antipole Tree [44], the M * -tree [76], and the CM-tree [47].…”

A cost model and index architecture for the similarity join

“…They present the VA-file, an improvement of the sequential scan. Ciaccia, Patella and Zezula [8] adapt the cost model in [6] to estimate the page accesses of M-trees, an index structure for data spaces which are metric spaces but not vector spaces (i.e. only the distances between the objects are known, but no explicit positions).…”

Deflating the dimensionality curse using multiple fractal dimensions

“…Selectivities for spatial joins using fractals are studied in [4]. Closer work to ours is that of [7] and [13], in which cost models for nearest neighbors are presented. In the former, assumptions of independence are implicit in the formulas.…”