Efficient Construction of Directed Hopsets and Parallel Approximate Shortest Paths

Explore the intricacies of directed hopsets and parallel approximate shortest paths in this 21-minute conference talk presented at the Association for Computing Machinery (ACM). Delve into the challenges of single-source shortest paths for directed graphs and discover how hopsets can be utilized to solve parallel shortest path problems. Learn about the definition and examples of inexact hopsets, previous research results, and the goals of the presented algorithm. Gain insights into algorithm preliminaries, path-related nodes, and the concept of bridge nodes. Understand the roles of pivots and shortcutters in distance-limited searches, and how to decrease search distances effectively. Conclude with an examination of far bridge pivots and their impact on efficient construction of directed hopsets.

Intro
Single Source Shortest Paths for Directed Graphs
Parallel Shortest Paths - Hopsets
Hopset: Definition
Inexact hopset example
Previous Results for Hopsets
Goal
Algorithm Preliminaries
The Algorithm for distance guess d
Path Related Nodes
Progress with recursion
Bridge nodes
Pivots and shortcutters
Distance limited search
Decrease search distance
Far bridge pivots
Conclusion