Data Structures on Event Graphs

TL;DR

This paper explores the behavior of data structures driven by event graphs, analyzing their limit behavior and providing algorithms for recognizing and efficiently handling operations in various walk scenarios.

Contribution

It introduces a model for data structures on event graphs, offering algorithms for recognition and efficient successor searching under different walk conditions.

Findings

Efficient algorithm for recognizing generated structures.

Near-optimal successor search algorithm for cycle event graphs with adversarial walks.

Optimal successor search algorithm for random walks.

Abstract

We investigate the behavior of data structures when the input and operations are generated by an event graph. This model is inspired by Markov chains. We are given a fixed graph G, whose nodes are annotated with operations of the type insert, delete and query. The algorithm responds to the requests as it encounters them during a (random or adversarial) walk in G. We study the limit behavior of such a walk and give an efficient algorithm for recognizing which structures can be generated. We also give a near-optimal algorithm for successor searching if the event graph is a cycle and the walk is adversarial. For a random walk, the algorithm becomes optimal.