Finding Top-k Dominance on Incomplete Big Data Using Map-Reduce Framework

Incomplete data is one major kind of multi-dimensional dataset that has random-distributed missing nodes in its dimensions. It is very difficult to retrieve information from this type of dataset when it becomes huge. Finding top-k dominant values in this type of dataset is a challenging procedure. Some algorithms are present to enhance this process but are mostly efficient only when dealing with a small-size incomplete data. One of the algorithms that make the application of TKD query possible is the Bitmap Index Guided (BIG) algorithm. This algorithm strongly improves the performance for incomplete data, but it is not originally capable of finding top-k dominant values in incomplete big data, nor is it designed to do so. Several other algorithms have been proposed to find the TKD query, such as Skyband Based and Upper Bound Based algorithms, but their performance is also questionable. Algorithms developed previously were among the first attempts to apply TKD query on incomplete data; however, all these had weak performances or were not compatible with the incomplete data. This thesis proposes MapReduced Enhanced Bitmap Index Guided Algorithm (MRBIG) for dealing with the aforementioned issues. MRBIG uses the MapReduce framework to enhance the performance of applying top-k dominance queries on huge incomplete datasets. The proposed approach uses the MapReduce parallel computing approach using multiple computing nodes. The framework separates the tasks between several computing nodes that independently and simultaneously work to find the result. This method has achieved up to two times faster processing time in finding the TKD query result in comparison to previously presented algorithms

Indexing the Earth Mover's Distance Using Normal Distributions

Querying uncertain data sets (represented as probability distributions) presents many challenges due to the large amount of data involved and the difficulties comparing uncertainty between distributions. The Earth Mover's Distance (EMD) has increasingly been employed to compare uncertain data due to its ability to effectively capture the differences between two distributions. Computing the EMD entails finding a solution to the transportation problem, which is computationally intensive. In this paper, we propose a new lower bound to the EMD and an index structure to significantly improve the performance of EMD based K-nearest neighbor (K-NN) queries on uncertain databases. We propose a new lower bound to the EMD that approximates the EMD on a projection vector. Each distribution is projected onto a vector and approximated by a normal distribution, as well as an accompanying error term. We then represent each normal as a point in a Hough transformed space. We then use the concept of stochastic dominance to implement an efficient index structure in the transformed space. We show that our method significantly decreases K-NN query time on uncertain databases. The index structure also scales well with database cardinality. It is well suited for heterogeneous data sets, helping to keep EMD based queries tractable as uncertain data sets become larger and more complex.Comment: VLDB201

String Searching with Ranking Constraints and Uncertainty

Strings play an important role in many areas of computer science. Searching pattern in a string or string collection is one of the most classic problems. Different variations of this problem such as document retrieval, ranked document retrieval, dictionary matching has been well studied. Enormous growth of internet, large genomic projects, sensor networks, digital libraries necessitates not just efficient algorithms and data structures for the general string indexing, but indexes for texts with fuzzy information and support for queries with different constraints. This dissertation addresses some of these problems and proposes indexing solutions. One such variation is document retrieval query for included and excluded/forbidden patterns, where the objective is to retrieve all the relevant documents that contains the included patterns and does not contain the excluded patterns. We continue the previous work done on this problem and propose more efficient solution. We conjecture that any significant improvement over these results is highly unlikely. We also consider the scenario when the query consists of more than two patterns. The forbidden pattern problem suffers from the drawback that linear space (in words) solutions are unlikely to yield a solution better than O(root(n/occ)) per document reporting time, where n is the total length of the documents and occ is the number of output documents. Continuing this path, we introduce a new variation, namely document retrieval with forbidden extension query, where the forbidden pattern is an extension of the included pattern.We also address the more general top-k version of the problem, which retrieves the top k documents, where the ranking is based on PageRank relevance metric. This problem finds motivation from search applications. It also holds theoretical interest as we show that the hardness of forbidden pattern problem is alleviated in this problem. We achieve linear space and optimal query time for this variation. We also propose succinct indexes for both these problems. Position restricted pattern matching considers the scenario where only part of the text is searched. We propose succinct index for this problem with efficient query time. An important application for this problem stems from searching in genomic sequences, where only part of the gene sequence is searched for interesting patterns. The problem of computing discriminating(resp. generic) words is to report all minimal(resp. maximal) extensions of a query pattern which are contained in at most(resp. at least) a given number of documents. These problems are motivated from applications in computational biology, text mining and automated text classification. We propose succinct indexes for these problems. Strings with uncertainty and fuzzy information play an important role in increasingly many applications. We propose a general framework for indexing uncertain strings such that a deterministic query string can be searched efficiently. String matching becomes a probabilistic event when a string contains uncertainty, i.e. each position of the string can have different probable characters with associated probability of occurrence for each character. Such uncertain strings are prevalent in various applications such as biological sequence data, event monitoring and automatic ECG annotations. We consider two basic problems of string searching, namely substring searching and string listing. We formulate these well known problems for uncertain strings paradigm and propose exact and approximate solution for them. We also discuss a constrained variation of orthogonal range searching. Given a set of points, the task of orthogonal range searching is to build a data structure such that all the points inside a orthogonal query region can be reported. We introduce a new variation, namely shared constraint range searching which naturally arises in constrained pattern matching applications. Shared constraint range searching is a special four sided range reporting query problem where two constraints has sharing among them, effectively reducing the number of independent constraints. For this problem, we propose a linear space index that can match the best known bound for three dimensional dominance reporting problem. We extend our data structure in the external memory model

Efficient Indexing for Structured and Unstructured Data

The collection of digital data is growing at an exponential rate. Data originates from wide range of data sources such as text feeds, biological sequencers, internet traffic over routers, through sensors and many other sources. To mine intelligent information from these sources, users have to query the data. Indexing techniques aim to reduce the query time by preprocessing the data. Diversity of data sources in real world makes it imperative to develop application specific indexing solutions based on the data to be queried. Data can be structured i.e., relational tables or unstructured i.e., free text. Moreover, increasingly many applications need to seamlessly analyze both kinds of data making data integration a central issue. Integrating text with structured data needs to account for missing values, errors in the data etc. Probabilistic models have been proposed recently for this purpose. These models are also useful for applications where uncertainty is inherent in data e.g. sensor networks. This dissertation aims to propose efficient indexing solutions for several problems that lie at the intersection of database and information retrieval such as joining ranked inputs, full-text documents searching etc. Other well-known problems of ranked retrieval and pattern matching are also studied under probabilistic settings. For each problem, the worst-case theoretical bounds of the proposed solutions are established and/or their practicality is demonstrated by thorough experimentation

Infinite Probabilistic Databases

Probabilistic databases (PDBs) are used to model uncertainty in data in a quantitative way. In the standard formal framework, PDBs are finite probability spaces over relational database instances. It has been argued convincingly that this is not compatible with an open-world semantics (Ceylan et al., KR 2016) and with application scenarios that are modeled by continuous probability distributions (Dalvi et al., CACM 2009). We recently introduced a model of PDBs as infinite probability spaces that addresses these issues (Grohe and Lindner, PODS 2019). While that work was mainly concerned with countably infinite probability spaces, our focus here is on uncountable spaces. Such an extension is necessary to model typical continuous probability distributions that appear in many applications. However, an extension beyond countable probability spaces raises nontrivial foundational issues concerned with the measurability of events and queries and ultimately with the question whether queries have a well-defined semantics. It turns out that so-called finite point processes are the appropriate model from probability theory for dealing with probabilistic databases. This model allows us to construct suitable (uncountable) probability spaces of database instances in a systematic way. Our main technical results are measurability statements for relational algebra queries as well as aggregate queries and Datalog queries