Michal Krátký

Implementation of XPath axes in the multi-dimensional approach to indexing XML data

XML (Extensible Mark-up Language) has been recently understood as a new approach to data modelling An implementation of a system enabling us to store and query XML documents efficiently requires the development of new techniques which make it possible to index an XML document in a way that provides an efficient evaluation of a user query Most XML query languages are based on the language XPath and use a form of path expressions for composing more general queries XPath defines a family of 13 axes, i.e relationship types in which an actual element can be associated to other elements in the XML tree Previously published multi-dimensional approaches to indexing XML data use paged and balanced multi-dimensional data structures like UB-trees and R*-trees In this paper we revise the approaches and introduce a novel approach to the implementation of an XPath subset.

Revisiting M-Tree Building Principles

The M-tree is a dynamic data structure designed to index metric datasets. In this paper we introduce two dynamic techniques of building the M-tree. The first one incorporates a multi-way object insertion while the second one exploits the generalized slim-down algorithm. Usage of these techniques or even combination of them significantly increases the querying performance of the M-tree. We also present comparative experimental results on large datasets showing that the new techniques outperform by far even the static bulk loading algorithm.

Fast decoding algorithms for variable-lengths codes

Data compression has been widely applied in many data processing areas. Compression methods use variable-length codes with the shorter codes assigned to symbols or groups of symbols that appear in the data frequently. There exist many coding algorithms, e.g. Elias-delta codes, Fibonacci codes and other variable-length codes which are often applied to encoding of numbers. Although we often do not consider time consumption of decompression as well as compression algorithms, there are cases where the decompression time is a critical issue. For example, a real-time compression of data structures, applied in the case of the physical implementation of database management systems, follows this issue. In this case, pages of a data structure are decompressed during every reading from a secondary storage into the main memory or items of a page are decompressed during every access to the page. Obviously, efficiency of a decompression algorithm is extremely important. Since fast decoding algorithms were not known until recently, variable-length codes have not been used in the data processing area. In this article, we introduce fast decoding algorithms for Elias-delta, Fibonacci of order 2 as well as Fibonacci of order 3 codes. We provide a theoretical background making these fast algorithms possible. Moreover, we introduce a new code, called the Elias-Fibonacci code, with a lower compression ratio than the Fibonacci of order 3 code for lower numbers; however, this new code provides a faster decoding time than other tested codes. Codes of Elias-Fibonacci are shorter than other compared codes for numbers longer than 26 bits. All these algorithms are suitable in the case of data processing tasks with special emphasis on the decompression time.

A new range query algorithm for universal B-trees

In multi-dimensional databases the essential tool for accessing data is the range query (or window query). In this paper we introduce a new algorithm of processing range query in universal B-tree (UB-tree), which is an index structure for searching in multi-dimensional databases. The new range query algorithm (called the DRU algorithm) works efficiently, even for processing high-dimensional databases. In particular, using the DRU algorithm many of the UB-tree inner nodes need not to be accessed. We explain the DRU algorithm using a simple geometric model, providing a clear insight into the problem. More specifically, the model exploits an interesting relation between the Z-curve and generalized quad-trees. We also present experimental results for the DRU algorithm implementation.

On the efficient search of an XML twig query in large DataGuide trees

XML (Extensible Mark-up Language) has been embraced as a new approach to data modeling. Nowadays, more and more information is formatted as semi-structured data, e.g., articles in a digital library, documents on the web, and so on. Implementation of an efficient system enabling storage and querying of XML documents requires development of new techniques. Many different techniques of XML indexing have been proposed in recent years. In the case of XML data, we can distinguish the following trees: an XML tree, a tree of elements and attributes, and a DataGuide, a tree of element tags and attribute names. Obviously, the XML tree of an XML document is much larger than the DataGuide of a given document. Authors often consider DataGuide as a small tree. Therefore, they consider the DataGuide search as a small problem. However, we show that DataGuide trees are often massive in the case of real XML documents. Consequently, a trivial DataGuide search may be time and memory consuming. In this article, we introduce efficient methods for searching an XML twig pattern in large, complex DataGuide trees.

The Geometric Framework for Exact and Similarity Querying XML Data

Using the terminology usual in databases, it is possible to view XML as a language for data modeling. To retrieve XML data from XML databases, several query languages have been proposed. The common feature of such languages is the use of regular path expressions. They enable the user to navigate through arbitrary long paths in XML data. If we considered a path content as a vector of path elements, we would be able to model XML paths as points within a multidimensional vector space. This paper introduces a geometric framework for indexing and querying XML data conceived in this way. In consequence, we can use certain data structures for indexing multidimensional points (objects). We use the UB-tree for indexing the vector spaces and the M-tree for indexing the metric spaces. The data structures for indexing the vector spaces lead rather to exact matching queries while the structures for indexing the metric spaces allow us to provide the similarity queries.

Optimal and efficient generalized twig pattern processing: a combination of preorder and postorder filterings

Searching for occurrences of a twig pattern query (TPQ) in an XML document is a core task of all XML database query languages. The generalized twig pattern (GTP) extends the TPQ model to include semantics related to output nodes, optional nodes, and boolean expressions which are part of the XQuery language. Preorder filtering holistic algorithms such as TwigStack represent a significant class of TPQ processing approaches with a linear worst-case I/O complexity with respect to the sum of the input and output sizes for some query classes. Another important class of holistic approaches is represented by postorder filtering holistic algorithms such as

Benchmarking the compression of XML node streams

\text{ Twig}^2