Efficient Online Processing for Advanced Analytics

With the advent of emerging technologies and the Internet of Things, the importance of online data analytics has become more pronounced. Businesses and companies are adopting approaches that provide responsive analytics to stay competitive in the global marketplace. Online analytics allow data analysts to promptly react to patterns or to gain preliminary insights from early results that aid in research, decision making, and effective strategy planning. The growth of data-velocity in a variety of domains including, high-frequency trading, social networks, infrastructure monitoring, and advertising require adopting online engines that can efficiently process continuous streams of data. This thesis presents foundations, techniques, and systems' design that extend the state-of-the-art in online query processing to efficiently support relational joins with arbitrary join-predicates (beyond traditional equi-joins); and to support other data models (beyond relational) that target machine learning and graph computations. The thesis is divided into two parts: We first present a brief overview of Squall, our open-source online query processing engine that supports SQL-like queries on top of streams. Then, we focus on extending Squall to support efficient theta-join processing. Scalable distributed join processing requires a partitioning policy that evenly distributes the processing load while minimizing the size of maintained state and duplicated messages. Efficient load-balance demands apriori-statistics which are not available in the online setting. We propose a novel operator that continuously adjusts itself to the data dynamics, through adaptive dataflow routing and state repartitioning. It is also resilient to data-skew, maintains high throughput rates, avoids blocking during state repartitioning, and behaves as a black-box dataflow operator with provable performance guarantees. Our evaluation demonstrates that the proposed operator outperforms the state-of-the-art static partitioning schemes in resource utilization, throughput, and execution time up to 7x. In the second part, we present a novel framework that supports the Incremental View Maintenance (IVM) of workloads expressed as linear algebra programs. Linear algebra represents a concrete substrate for advanced analytical tasks including, machine learning, scientific computation, and graph algorithms. Previous works on relational calculus IVM are not applicable to matrix algebra workloads. This is because a single entry change to an input-matrix results in changes all over the intermediate views, rendering IVM useless in comparison to re-evaluation. We present Lago, a unified modular compiler framework that supports the IVM of a broad class of linear algebra programs. Lago automatically derives and optimizes incremental trigger programs of analytical computations, while freeing the user from erroneous manual derivations, low-level implementation details, and performance tuning. We present a novel technique that captures $\Delta$ changes as low-rank matrices. Low-rank matrices are representable in a compressed factored form that enables cheaper computations. Lago automatically propagates the factored representation across program statements to derive an efficient trigger program. Moreover, Lago extends its support to other domains that use different semi-ring configurations, e.g., graph applications. Our evaluation results demonstrate orders of magnitude (10x-1

Semigroup congruences : computational techniques and theoretical applications

Computational semigroup theory is an area of research that is subject to growing interest. The development of semigroup algorithms allows for new theoretical results to be discovered, which in turn informs the creation of yet more algorithms. Groups have benefitted from this cycle since before the invention of electronic computers, and the popularity of computational group theory has resulted in a rich and detailed literature. Computational semigroup theory is a less developed field, but recent work has resulted in a variety of algorithms, and some important pieces of software such as the Semigroups package for GAP. Congruences are an important part of semigroup theory. A semigroup’s congruences determine its homomorphic images in a manner analogous to a group’s normal subgroups. Prior to the work described here, there existed few practical algorithms for computing with semigroup congruences. However, a number of results about alternative representations for congruences, as well as existing algorithms that can be borrowed from group theory, make congruences a fertile area for improvement. In this thesis, we first consider computational techniques that can be applied to the study of congruences, and then present some results that have been produced or precipitated by applying these techniques to interesting examples. After some preliminary theory, we present a new parallel approach to computing with congruences specified by generating pairs. We then consider alternative ways of representing a congruence, using intermediate objects such as linked triples. We also present an algorithm for computing the entire congruence lattice of a finite semigroup. In the second part of the thesis, we classify the congruences of several monoids of bipartitions, as well as the principal factors of several monoids of partial transformations. Finally, we consider how many congruences a finite semigroup can have, and examine those on semigroups with up to seven elements

Proceedings of the 26th International Symposium on Theoretical Aspects of Computer Science (STACS'09)

The Symposium on Theoretical Aspects of Computer Science (STACS) is held alternately in France and in Germany. The conference of February 26-28, 2009, held in Freiburg, is the 26th in this series. Previous meetings took place in Paris (1984), Saarbr¨ucken (1985), Orsay (1986), Passau (1987), Bordeaux (1988), Paderborn (1989), Rouen (1990), Hamburg (1991), Cachan (1992), W¨urzburg (1993), Caen (1994), M¨unchen (1995), Grenoble (1996), L¨ubeck (1997), Paris (1998), Trier (1999), Lille (2000), Dresden (2001), Antibes (2002), Berlin (2003), Montpellier (2004), Stuttgart (2005), Marseille (2006), Aachen (2007), and Bordeaux (2008). ..