Improved Periodicity Mining in Time Series Databases

Time series data represents information about real world phenomena and periodicity mining explores the interesting periodic behavior that is inherent in the data. Periodicity mining has numerous applications such as in weather forecasting, stock market prediction and analysis, pattern recognition, etc. Recently, the suffix tree, a powerful data structure that efficiently solves many strings related problems has been used to gather information about repeated substrings in the text and then perform periodicity mining. However, periodicity mining deals with large amounts of data which makes it difficult to perform mining in main memory due to the space constraints of the suffix tree. Thus, we first propose the use of the Compressed Suffix Tree (CST) for space efficient periodicity mining in very large datasets. Given the time-space trade-off that comes with any practical usage of the CST, we provide a comprehensive empirical analysis on the practical usage of CSTs and traditional suffix trees for periodicity mining.;Noise is an inherent part of practical time series data, and it is important to mine periods in spite of the noise. This leads to the problem of approximate periodicity mining. Existing algorithms have dealt with the noise introduced between the occurrences of the periodic pattern, but not the noise introduced in the structure of the pattern itself. We present a taxonomy for approximate periodicity and then propose an algorithm that performs periodicity mining in the presence of noise introduced simultaneously in both the structure of the pattern and between the periodic occurrences of the pattern

Data Structures for Efficient String Algorithms

This thesis deals with data structures that are mostly useful in the area of string matching and string mining. Our main result is an O(n)-time preprocessing scheme for an array of n numbers such that subsequent queries asking for the position of a minimum element in a specified interval can be answered in constant time (so-called RMQs for Range Minimum Queries). The space for this data structure is 2n+o(n) bits, which is shown to be asymptotically optimal in a general setting. This improves all previous results on this problem. The main techniques for deriving this result rely on combinatorial properties of arrays and so-called Cartesian Trees. For compressible input arrays we show that further space can be saved, while not affecting the time bounds. For the two-dimensional variant of the RMQ-problem we give a preprocessing scheme with quasi-optimal time bounds, but with an asymptotic increase in space consumption of a factor of log(n). It is well known that algorithms for answering RMQs in constant time are useful for many different algorithmic tasks (e.g., the computation of lowest common ancestors in trees); in the second part of this thesis we give several new applications of the RMQ-problem. We show that our preprocessing scheme for RMQ (and a variant thereof) leads to improvements in the space- and time-consumption of the Enhanced Suffix Array, a collection of arrays that can be used for many tasks in pattern matching. In particular, we will see that in conjunction with the suffix- and LCP-array 2n+o(n) bits of additional space (coming from our RMQ-scheme) are sufficient to find all occ occurrences of a (usually short) pattern of length m in a (usually long) text of length n in O(m*s+occ) time, where s denotes the size of the alphabet. This is certainly optimal if the size of the alphabet is constant; for non-constant alphabets we can improve this to O(m*log(s)+occ) locating time, replacing our original scheme with a data structure of size approximately 2.54n bits. Again by using RMQs, we then show how to solve frequency-related string mining tasks in optimal time. In a final chapter we propose a space- and time-optimal algorithm for computing suffix arrays on texts that are logically divided into words, if one is just interested in finding all word-aligned occurrences of a pattern. Apart from the theoretical improvements made in this thesis, most of our algorithms are also of practical value; we underline this fact by empirical tests and comparisons on real-word problem instances. In most cases our algorithms outperform previous approaches by all means

Algoritmi efficienti per la scoperta di pattern ripetuti a intervalli

Dal momento che non esiste ancora sufficiente conoscenza per costruire un adeguato modello dell'informazione, e tale da filtrare sequenze di caratteri rilevanti da altre apparentemente senza significato, si ricorre spesso ad approcci che non prevedono l'uso di un modello di dati. La formulazione di notazioni massimali, senza introdurre perdita d'informazione, cattura importanti caratteristiche sulla struttura interna dei motif e ne riduce drasticamente il numero da analizzare, conferendo un senso all'enorme numero di risultati. In questa tesi propongo un approccio alla codifica delle sequenze nucleotidiche altamente ridondanti, tale da produrre permutazioni numeriche. Questa metodologia, che usa i Suffix Tree, mira a generare codifiche esenti da alterazioni o artefatti dell'informazione genetica producendo, per design, permutazioni "compatibili" con i minimal consensus PQ Tree, i quali sono usati per la creazione della notazione massimale. Si forniscono le motivazioni che hanno ispirato questo approccio, basato sull'analisi della struttura permutativa interna delle stringhe. Si delineano alcuni possibili sviluppi e si forniscono molti esempi accompagnati da un caso d'uso reale

Storage and aggregation for fast analytics systems

Computing in the last decade has been characterized by the rise of data- intensive scalable computing (DISC) systems. In particular, recent years have wit- nessed a rapid growth in the popularity of fast analytics systems. These systems exemplify a trend where queries that previously involved batch-processing (e.g., run- ning a MapReduce job) on a massive amount of data, are increasingly expected to be answered in near real-time with low latency. This dissertation addresses the problem that existing designs for various components used in the software stack for DISC sys- tems do not meet the requirements demanded by fast analytics applications. In this work, we focus specifically on two components: 1. Key-value storage: Recent work has focused primarily on supporting reads with high throughput and low latency. However, fast analytics applications require that new data entering the system (e.g., new web-pages crawled, currently trend- ing topics) be quickly made available to queries and analysis codes. This means that along with supporting reads efficiently, these systems must also support writes with high throughput, which current systems fail to do. In the first part of this work, we solve this problem by proposing a new key-value storage system – called the WriteBuffer (WB) Tree – that provides up to 30× higher write per- formance and similar read performance compared to current high-performance systems. 2. GroupBy-Aggregate: Fast analytics systems require support for fast, incre- mental aggregation of data for with low-latency access to results. Existing techniques are memory-inefficient and do not support incremental aggregation efficiently when aggregate data overflows to disk. In the second part of this dis- sertation, we propose a new data structure called the Compressed Buffer Tree (CBT) to implement memory-efficient in-memory aggregation. We also show how the WB Tree can be modified to support efficient disk-based aggregation.Ph.D

Lossless Differential Compression for Synchronizing Arbitrary Single-Dimensional Strings

Differential compression allows expressing a modified document as differences relative to another version of the document. A compressed string requires space relative to amount of changes, irrespective of original document sizes. The purpose of this study was to answer what algorithms are suitable for universal lossless differential compression for synchronizing two arbitrary documents either locally or remotely. Two main problems in differential compression are finding the differences (differencing), and compactly communicating the differences (encoding). We discussed local differencing algorithms based on subsequence searching, hashtable lookups, suffix searching, and projection. We also discussed probabilistic remote algorithms based on both recursive comparison and characteristic polynomial interpolation of hashes computed from variable-length content-defined substrings. We described various heuristics for approximating optimal algorithms as arbitrary long strings and memory limitations force discarding information. Discussion also included compact delta encoding and in-place reconstruction. We presented results from empirical testing using discussed algorithms. The conclusions were that multiple algorithms need to be integrated into a hybrid implementation, which heuristically chooses algorithms based on evaluation of the input data. Algorithms based on hashtable lookups are faster on average and require less memory, but algorithms based on suffix searching find least differences. Interpolating characteristic polynomials was found to be too slow for general use. With remote hash comparison, content-defined chunks and recursive comparison can reduce protocol overhead. A differential compressor should be merged with a state-of-art non-differential compressor to enable more compact delta encoding. Input should be processed multiple times to allow constant a space bound without significant reduction in compression efficiency. Compression efficiently of current popular synchronizers could be improved, as our empiral testing showed that a non-differential compressor produced smaller files without having access to one of the two strings

Engineering a compressed suffix tree implementation

Välimäki N, Mäkinen V, Gerlach W, Dixit K. Engineering a compressed suffix tree implementation. Journal of Experimental Algorithmics (JEA). 2009;14:4.2-2:4.23

Engineering a Compressed Suffix Tree Implementation

Välimäki N, Gerlach W, Dixit K, Mäkinen V. Engineering a Compressed Suffix Tree Implementation. In: Proceedings of 6th Workshop on Experimental Algorithms (WEA'07). Springer-Verlag; 2007: 217-228