During the past decades significant efforts have been made to propose data structures for answering connectivity queries on fully dynamic graphs, i.e., graphs with frequent insertions and deletions of edges. However, a comprehensive understanding of how these data structures perform in practice is missing, since not all of them have been implemented, let alone evaluated experimentally. We provide reference implementations for the proposed data structures and experimentally evaluate them on a wide range of graphs. Our findings show that the current solutions are not ready to be deployed in systems as is, as every data structure has critical weaknesses when used in practice. Key limitations that must be overcome are the space and time overhead incurred by balanced data structures, the degeneration of the runtime of space-efficient data structures in worst case scenarios, and the maintenance costs for balanced data structures. We detail our findings in the experimental evaluation and provide recommendations for implementing robust solutions for answering connectivity queries on dynamic graphs.

The intrinsic predictability of a given time series indicates how well an (ideal) algorithm could potentially predict it when trained on the time series data. Being able to compute the intrinsic predictability helps the developers of prediction algorithms immensely in deciding whether there is further optimization potential, as it tells them how close they are to what is (theoretically) achievable. We call the intrinsic predictability the predictability upper bound ¶imax and propose a novel method for quantifying and estimating it for univariate numeric time series. So far, this has only been done for symbolic time series, even though most real-world time series are numeric by nature. We base our technique on the close relationship between entropy and predictability, utilizing the entropy rate of a time series to compute ¶imax . Since existing entropy rate estimators, such as those based on the Lempel-Ziv compression algorithm, only work for symbolic data, we develop new estimators using tolerance thresholds for matching numeric values. We demonstrate that ¶imax is an effective upper bound that characterizes the intrinsic predictability of a time series. We give formal proofs and we validate our arguments experimentally by comparing ¶imax with the prediction accuracy of different state-of-the-art models on various real-world datasets from different domains.

A common analysis task over a stream of time series is to find all pairs of windows whose correlation is above a given threshold. For a large number of streams, doing so naively, i.e., checking the Cartesian product, is too expensive. In essence, finding correlated pairs in a non-naive way boils down to a high-dimensional similarity join in a Euclidean space. While there are similarity join algorithms, such as Quickjoin and ε-kdB tree, they are inefficient for high-dimensional data. We propose CorrJoin, short for Correlation Join, that combines a complementary dimension reduction and transformation step with a subsequent double-filtering step. In the first step, we reduce the dimensionality of data stream windows by combining a fast but inaccurate method, Piecewise Aggregate Approximation (PAA), with an accurate and slow one, Singular Value Decomposition (SVD). Not only does SVD compensate for the weaknesses of PAA, it also transforms the data to make the first filter based on bucketing more effective. The second filter, which uses Euclidean distances, reduces the number of false positives before computing exact correlations. Our experiments reveal that in common settings, CorrJoin is an order of magnitude faster than state-of-the-art approaches (up to 20 times faster than Quickjoin).

Abstract Frequent queries on semi-structured hierarchical data are Content-and-Structure (CAS) queries that filter data items based on their location in the hierarchical structure and their value for some attribute. We propose the Robust and Scalable Content-and-Structure (RSCAS) index to efficiently answer CAS queries on big semi-structured data. To get an index that is robust against queries with varying selectivities, we introduce a novel dynamic interleaving that merges the path and value dimensions of composite keys in a balanced manner. We store interleaved keys in our trie-based RSCAS index, which efficiently supports a wide range of CAS queries, including queries with wildcards and descendant axes. We implement RSCAS as a log-structured merge tree to scale it to data-intensive applications with a high insertion rate. We illustrate RSCAS’s robustness and scalability by indexing data from the Software Heritage (SWH) archive, which is the world’s largest, publicly available source code archive.

Answering connectivity queries is fundamental to fully dynamic graphs where edges and vertices are inserted and deleted frequently. Existing work proposes data structures and algorithms with worst case guarantees. We propose a new data structure, the dynamic tree (D-tree), together with algorithms to construct and maintain it. The D-tree is the first data structure that scales to fully dynamic graphs with millions of vertices and edges and, on average, answers connectivity queries much faster than data structures with worst case guarantees.

Abstract The humanities, like many other areas of society, are currently undergoing major changes in the wake of digital transformation. However, in order to make collection of digitised material in this area easily accessible, we often still lack adequate search functionality. For instance, digital archives for textiles offer keyword search, which is fairly well understood, and arrange their content following a certain taxonomy, but search functionality at the level of thread structure is still missing. To facilitate the clustering and search, we introduce an approach for recognising similar weaving patterns based on their structures for textile archives. We first represent textile structures using hypergraphs and extract multisets of k-neighbourhoods describing weaving patterns from these graphs. Then, the resulting multisets are clustered using various distance measures and various clustering algorithms (K-Means for simplicity and hierarchical agglomerative algorithms for precision). We evaluate the different variants of our approach experimentally, showing that this can be implemented efficiently (meaning it has linear complexity), and demonstrate its quality to query and cluster datasets containing large textile samples. As, to the best of our knowledge, this is the first practical approach for explicitly modelling complex and irregular weaving patterns usable for retrieval, we aim at establishing a solid baseline.

Abstract We develop a family of efficient plane-sweeping interval join algorithms for evaluating a wide range of interval predicates such as Allen’s relationships and parameterized relationships. Our technique is based on a framework, components of which can be flexibly combined in different manners to support the required interval relation. In temporal databases, our algorithms can exploit a well-known and flexible access method, the Timeline Index, thus expanding the set of operations it supports even further. Additionally, employing a compact data structure, the gapless hash map, we utilize the CPU cache efficiently. In an experimental evaluation, we show that our approach is several times faster and scales better than state-of-the-art techniques, while being much better suited for real-time event processing.

We propose a robust index for semi-structured hierarchical data that supports content-and-structure (CAS) queries specified by path and value predicates. At the heart of our approach is a novel dynamic interleaving scheme that merges the path and value dimensions of composite keys in a balanced way. We store these keys in our trie-based Robust Content-And-Structure index, which efficiently supports a wide range of CAS queries, including queries with wildcards and descendant axes. Additionally, we show important properties of our scheme, such as robustness against varying selectivities, and demonstrate improvements of up to two orders of magnitude over existing approaches in our experimental evaluation.

We present a framework for high-level event detection in video streams based on a novel temporal extension of relational algebra. With the help of intuitive and interactive graphical user interfaces, a user can have a look at the different layers of our system to gain insights into the inner workings of the system, as well as create new events on the fly and track their processing through the system. As a proof-of-concept we have predefined events on three video surveillance data sets, but we also plan to run a demo with a live video stream generated by a local webcam.

We develop an approach for solving rooted orienteering problems with category constraints as found in tourist trip planning and logistics. It is based on expanding partial solutions in a systematic way, prioritizing promising ones, which reduces the search space we have to traverse during the search. The category constraints help in reducing the space we have to explore even further. We implement an algorithm that computes the optimal solution and also illustrate how our approach can be turned into an anytime approximation algorithm, yielding much faster run times and guaranteeing lower bounds on the quality of the solution found. We demonstrate the effectiveness of our algorithms by comparing them to the state-of-the-art approach and an optimal algorithm based on dynamic programming, showing that our technique clearly outperforms these methods. These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

We develop an algorithm for efficiently joining relations on interval-based attributes with overlap predicates, which, for example, are commonly found in temporal databases. Using a new data structure and a lazy evaluation technique, we are able to achieve impressive performance gains by optimizing memory accesses exploiting features of modern CPU architectures. In an experimental evaluation with real-world datasets our algorithm is able to outperform the state-of-the-art by an order of magnitude.

The efficient computation of set containment joins (SCJ) over set-valued attributes is a well-studied problem with many applications in commercial and scientific fields. Nevertheless, there still exists a number of open questions: An extensive comparative evaluation is still missing, the two most recent algorithms have not yet been compared to each other, and the exact impact of item sort order and properties of the data on algorithms performance still is largely unknown. Furthermore, all previous works only considered sequential join algorithms, although modern servers offer ample opportunities for parallelization.

Optimising queries in real-world situations under imperfect conditions is still a problem that has not been fully solved. We consider finding the optimal order in which to execute a given set of selection operators under partial ignorance of their selectivities. The selectivities are modelled as intervals rather than exact values and we apply a concept from decision theory, the minimisation of the maximum regret, as a measure of optimality. The associated decision problem turns out to be NP-hard, which renders a brute-force approach to solving it impractical. Nevertheless, by investigating properties of the problem and identifying special cases which can be solved in polynomial time, we gain insight that we use to develop a novel heuristic for solving the general problem. We also evaluate minmax regret query optimisation experimentally, showing that it outperforms a currently employed strategy of optimisers that uses mean values for uncertain parameters.

We propose a novel approach for measuring the similarity between weaving patterns that can provide similarity-based search functionality for textile archives. We represent textile structures using hypergraphs and extract multisets of $k$-neighborhoods from these graphs. The resulting multisets are then compared using Jaccard coefficients, Hamming distances, and cosine measures. We evaluate the different variants of our similarity measure experimentally, showing that it can be implemented efficiently and illustrating its quality using it to cluster and query a data set containing more than a thousand textile samples.

We propose a more realistic approach to trip planning for tourist applications by adding category information to points of interest (POIs). This makes it easier for tourists to formulate their preferences by stating constraints on categories rather than individual POIs. However, solving this problem is not just a matter of extending existing algorithms. In our approach we exploit the fact that POIs are usually not evenly distributed but tend to appear in clusters. We develop a group of efficient algorithms based on clustering with guaranteed theoretical bounds. We also evaluate our algorithms experimentally, using real-world data sets, showing that in practice the results are better than the theoretical guarantees and very close to the optimal solution.

The XPath language incorporates powerful primitives for formulating queries containing nested subexpressions which are existentially or universally quantified. However, even the best published approaches for evaluating XPath have unsatisfactory performance when applied to nested queries. We examine optimization techniques that unnest complex XPath queries. For this purpose, we classify XPath expressions particularly with regard to properties that are relevant for unnesting. We present algebraic equivalences that transform nested expressions into unnested expressions. In our experiments we compare the evaluation times with existing XPath evaluators and the naive evaluation.

Queries formulated in a nested way are very common in XQuery. Unfortunately, their evaluation is usually very inefficient when done in a straightforward fashion. We present a framework for handling nested queries that is based on unnesting the queries after having translated them into an algebra. We not only present a collection of algebraic equivalences, but also supply a strategy on how to use them effectively. The full potential of the approach is demonstrated by applying our rewrites to actual queries and showing that performance gains of several orders of magnitude are possible.

We present the first complete translation of XPath into an algebra, paving the way for a comprehensive, state-of-the-art XPath (and later on, XQuery) compiler based on algebraic optimization techniques. Our translation includes all XPath features such as nested expressions, position-based predicates and node-set functions. The translated algebraic expressions can be executed using the proven, scalable, iterator-based approach, as we demonstrate in form of a corresponding physical algebra in our native XML DBMS Natix. A first glance at performance results shows that even without further optimization of the expressions, we provide a competitive evaluation technique for XPath queries.

The query optimizer of a database system is confronted with two aspects when handling user-defined functions (UDFs) in query predicates: the vast differences in evaluation costs between UDFs (and other functions) and multiple calls of the same (expensive) UDF The former is dealt with by ordering the evaluation of the predicates optimally, the latter by identifying common subexpressions and thereby avoiding costly recomputation. Current approaches order n predicates optimally (neglecting factorization) in O(nlogn). Their result may deviate significantly from the optimal solution under factorization. We formalize the problem of finding optimal orderings under factorization and prove that it is NP-hard. Furthermore, we show how to improve on the run time of the brute-force algorithm (which computes all possible orderings) by presenting different enhanced algorithms. Although in the worst case these algorithms obviously still behave exponentially, our experiments demonstrate that for real-life examples their performance is much better.

We present algebraic equivalences that allow to unnest nested algebraic expressions for order-preserving algebraic operators. We illustrate how these equivalences can be applied successfully to unnest nested queries given in the XQuery language. Measurements illustrate the performance gains possible by unnesting.

We present algebraic equivalences that allow to unnest nested algebraic expressions containing quantifiers for order-preserving algebraic operators. We illustrate how these equivalences can be applied successfully to unnest nested queries formulated in XQuery. Measurements illustrate the performance gains possible by unnesting.

We propose a new approach for the efficient evaluation of XPath expressions. This is important, since XPath is not only used as a simple, stand-alone query language, but is also an essential ingredient of XQuery and XSLT. The main idea of our approach is to translate XPath into algebraic expressions parameterized with programs. These programs are mainly built from navigational primitives like accessing the first child or the next sibling. The goals of the approach are: 1) to enable pipelined evaluation, 2) to avoid producing duplicate (intermediate) result nodes, 3) to visit as few document nodes as possible, and 4) to avoid visiting nodes more than once. This improves the existing approaches, because our method is highly efficient.