Technology Category
Search and Optimization: Distributed SearchData Mining & Knowledge Management: Graph Mining, Social Network Analysis & CommunityPlanning, Routing, and Scheduling: Optimization of Spatio-temporal Systems
Fully Dynamic Breadth First Search and Spanning Trees in Directed Graphs
🤖 AI Summary
This work addresses the challenge of efficiently maintaining breadth-first search (BFS) structures under dynamic edge insertions and deletions in directed graphs. It presents the first fully dynamic BFS framework that simultaneously preserves the BFS spanning tree, node levels, and BFS ordering. By integrating novel dynamic data structures with incremental update strategies, the approach cohesively handles the impact of edge modifications on single-source shortest paths and reachability. This study bridges a critical gap in the theoretical understanding of fully dynamic BFS for directed graphs and provides both foundational insights and practical tools for dynamic graph algorithms.
Technology Category
Application Category
📝 Abstract
We study the problem of maintaining a breadth-first spanning tree and the induced BFS ordering in a directed graph under edge updates. While semi-dynamic algorithms are known, maintaining the spanning tree, level information, and numbering together in the fully dynamic setting is less developed. This preprint presents a framework for fully dynamic BFS in directed graphs together with supporting data structures for maintaining the BFS tree, single-source shortest paths, and single-source reachability under both insertions and deletions.
Problem
Research questions and friction points this paper is trying to address.
Fully Dynamic
Breadth First Search
Directed Graphs
Spanning Trees
Edge Updates
Innovation
Methods, ideas, or system contributions that make the work stand out.
fully dynamic
breadth-first search
directed graphs
spanning trees
single-source reachability
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2024-01-04arXiv.orgCitations: 0
