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