An experimental comparison of tree-data structures for connectivity queries on fully-dynamic undirected graphs (Extended Version)

TL;DR

This paper provides an experimental comparison of various tree-based data structures for connectivity queries on fully dynamic undirected graphs, revealing practical limitations and offering insights for robust implementation.

Contribution

It offers the first comprehensive experimental evaluation of existing data structures for dynamic connectivity, highlighting their weaknesses and providing practical recommendations.

Findings

Current data structures have significant space and time overheads.

Performance degrades in worst-case scenarios for space-efficient structures.

Maintenance costs are high for balanced data structures.

Abstract

During the past decades significant efforts have been made to propose data structures for answering connectivity queries on fully dynamic graphs, i.e., graphs with frequent insertions and deletions of edges. However, a comprehensive understanding of how these data structures perform in practice is missing, since not all of them have been implemented, let alone evaluated experimentally. We provide reference implementations for the proposed data structures and experimentally evaluate them on a wide range of graphs. Our findings show that the current solutions are not ready to be deployed in systems as is, as every data structure has critical weaknesses when used in practice. Key limitations that must be overcome are the space and time overhead incurred by balanced data structures, the degeneration of the runtime of space-efficient data structures in worst case scenarios, and the maintenance costs for balanced data structures. We detail our findings in the experimental evaluation and provide recommendations for implementing robust solutions for answering connectivity queries on dynamic graphs.