Magíster en Ciencias, Mención Computación / El principal objetivo de esta tesis es encontrar casos tratables y buenas técnicas para computar Certain Answers sobre bases de datos de grafos incompletas, en tiempo polinomial. Las bases de datos de grafos surgen naturalmente de la necesidad de almacenar información de redes, tales como Facebook, mapas de rutas o la web. La idea de "incompletitud" viene de la falta de información completa, complejidad con la cual tenemos que trabajar a diario. Sobre estas bases de datos de grafos carentes de información completa, queremos realizar preguntas en la forma de consultas particulares y determinar si la pregunta puede ser contestada de la misma forma en cada posible completación de la base de datos. La respuesta a estas preguntas en cada posible completación de una base de datos de grafos incompleta es llamada Certain Answers. El problema de Certain Answers sobre bases de datos de grafos incompletas ya ha sido estudiado, y es conocido que este problema es en general co-NP completo. En esta tesis convertimos el problema de computar Certain Answers en un problema 3-SAT con su fórmula lógica booleana asociada. Podemos probar que bajo ciertas condiciones esta fórmula lógica tiene un número de variables que nos permite determinar si es satisfacible en tiempo polinomial. Luego, probamos que estas condiciones son exhaustivas: sin cualquiera de ellas el problema se vuelve co-NP completo otra vez. Para analizar más clases tratables del problema de Certain Answers, convertimos el problema Certain Answers en un problema de programación lineal entera. Con esta formulación de programación lineal, encontramos algunos casos tratables, algoritmos y heurísticas para resolverlo. Sin embargo, el principal logro es la nueva formulación en sí, porque nos permite usar las bien conocidas técnicas de programación lineal para encontrar más casos tratables y mejores heurísticas.

Graph-structured data (GSD) is a popular model to represent complex information in a wide variety of applications such as social networks, biological data management, digital libraries, and traffic networks. The flexibility of this model allows the information to evolve and easily integrate with heterogeneous data from many sources. In this dissertation we study three important problems on GSD. A consistent theme of our work is the use of automata methods and techniques to process and reason about GSD. First, we address the problem of answering queries on GSD in a distributed environment. We focus on regular path queries (RPQs) – given by regular expressions matching paths in graph-data. RPQs are the building blocks of almost any mechanism for querying GSD. We present a fault-tolerant, message-efficient, and truly distributed algorithm for answering RPQs. Our algorithm works for the larger class of weighted RPQs on weighted GSDs. Second, we consider the problem of answering RPQs on incomplete GSD, where different data sources are represented by materialized database views. We explore the connection between “certain answers” (CAs) and answers obtained from “view-based rewritings” (VBRs) for RPQs. CAs are answers that can be obtained on each database consistent with the views. Computing all of CAs for RPQs is NP-hard, and one has to resort to an exponential algorithm in the size of the data–view materializations. On the other hand, VBRs are query reformulations in terms of the view definitions. They can be used to obtain query answers in polynomial time in the size of the data. These answers are CAs, but unfortunately for RPQs, not all of the CAs can be obtained in this way. In this work, we show the surprising result that for RPQs under local semantics, using VBRs to answer RPQs gives all the CAs. The importance of this result is that under such semantics, the CAs can be obtained in polynomial time in the size of the data. Third, we focus on XML–an important special case of GSD. The scenario we consider is streaming XML between exchanging parties. The problem we study is flexible validation of streaming XML under the realistic assumption that the schemas of the exchanging parties evolve, and thus diverge from one another. We represent schemas by using Visibly Pushdown Automata (VPAs), which recognize Visibly Pushdown Languages (VPLs). We model evolution for XML by defining formal language operators on VPLs. We show that VPLs are closed under the defined language operators and this enables us to expand the schemas (for XML) in order to account for flexible or constrained evolution. / Graduate