Reachability and Distances under Multiple Changes

Recently it was shown that the transitive closure of a directed graph can be updated using first-order formulas after insertions and deletions of single edges in the dynamic descriptive complexity framework by Dong, Su, and Topor, and Patnaik and Immerman. In other words, Reachability is in DynFO. In this article we extend the framework to changes of multiple edges at a time, and study the Reachability and Distance queries under these changes. We show that the former problem can be maintained in DynFO(+, x) under changes affecting O({log n}/{log log n}) nodes, for graphs with n nodes. If the update formulas may use a majority quantifier then both Reachability and Distance can be maintained under changes that affect O(log^c n) nodes, for fixed c in N. Some preliminary results towards showing that distances are in DynFO are discussed

Global Semantic Integrity Constraint Checking for a System of Databases

In today’s emerging information systems, it is natural to have data distributed across multiple sites. We define a System of Databases (SyDb) as a collection of autonomous and heterogeneous databases. R-SyDb (System of Relational Databases) is a restricted form of SyDb, referring to a collection of relational databases, which are independent. Similarly, X-SyDb (System of XML Databases) refers to a collection of XML databases. Global integrity constraints ensure integrity and consistency of data spanning multiple databases. In this dissertation, we present (i) Constraint Checker, a general framework of a mobile agent based approach for checking global constraints on R-SyDb, and (ii) XConstraint Checker, a general framework for checking global XML constraints on X-SyDb. Furthermore, we formalize multiple efficient algorithms for varying semantic integrity constraints involving both arithmetic and aggregate predicates. The algorithms take as input an update statement, list of all global semantic integrity constraints with arithmetic predicates or aggregate predicates and outputs sub-constraints to be executed on remote sites. The algorithms are efficient since (i) constraint check is carried out at compile time, i.e. before executing update statement; hence we save time and resources by avoiding rollbacks, and (ii) the implementation exploits parallelism. We have also implemented a prototype of systems and algorithms for both R-SyDb and X-SyDb. We also present performance evaluations of the system

Introduction and Comparison of Dynamic Complexity Classes

This thesis gives some background and an introduction on dynamic complexity theory, a subfield of descriptive complexity theory in which queries on databases are maintained dynamically upon insertions and deletions to the database. The basic definitions of the dynamic complexity framework are given along with examples of queries maintainable with dynamic queries and a comparison of different dynamic complexity classes