The goal of this research project is to design, analyze and simulate restartable algorithms for on-line reorganization in parallel database management systems (DBMSs). The approach includes the description of explicit logging operations to assure consistency and preserve incremental improvements in the face of possible system failures at any site. Each algorithm is carefully detailed to work with standard concurrency and recovery modules in large DBMSs. Most large databases will soon be managed by parallel DBMSs (i.e., DBMSs on clusters of workstations, each managing its own collections of disks, connected by LANs and running the same software), so parallel algorithms are important. Earlier work in a centralized setting, by the Prof. Salzberg and her students Chendong Zou and Allyn Dimock, included algorithms for shrinking sparsely populated B-trees and for moving records (for example, to improve clustering). This project continues this work and expands it to a parallel setting. The project investigates the question of incrementally and lazily updating distributed dictionaries and indexes when records are moved from disks at one site to disks at another. This project represents the only work on on-line reorganization done in an academic setting which considers recovery and logging. Prof. Salzberg collaborates with Svein-Olaf Hvasshovd and Svein-Eric Bratsberg of Telenor Research (Norway's telephone company) using the parallel DBMS ClustRa as a testbed for the algorithmic work. Because this project considers recovery and because of the industrial collaboration, the results of this research are likely to able to be used in online reorganization utilities in commercial parallel DBMSs. ?