Active Data Structures and Applications to Dynamic and Kinetic Algorithms

We propose and study a novel data-structuring paradigm, called active data structures. Like a time machine, active data structures allow changes to occur not only in the present but at any point in time—including the past. Unlike most time machines, where changes to the past are incorporated and propagated automatically by magic, active data structures systematically communicate with the affected parties, prompting them to take appropriate actions. We demonstrate an efficient maintenance of three active data structures: (monotone) priority queue, dictionary, and compare-and-swap. These data structures, when paired with the self-adjusting computation framework, create new possibilities in kinetic and dynamic algorithms engineering. Based on this interaction, we present three practical algorithms: a new algorithm for 3-d kinetic/dynamic convex hull, an algorithm for dynamic list-sorting, and an algorithm for dynamic single-source shortest-path (based on Dijkstra). Our 3-d kinetic convex hull is the first efficient kinetic 3-d convex hull algorithm that supports dynamic changes simultaneously. This thesis provides an implementation for selected active data structures and applications, whose performance is analyzed both theoretically and experimentally.