2022/01/09 by Soheil Behnezhad, Sanjeev Khanna, Behnezhad, Soheil +1 · 2 citations
Computer Science · #Complexity and Algorithms in Graphs #Data Structures and Algorithms (cs.DS) #FOS: Computer and information sciences #Graph Theory and Algorithms #Network Packet Processing and Optimization
paper · pdf · doi:10.48550/arxiv.2201.02905
openalex publication_date 2022/01/09 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We study the maximum matching problem in fully dynamic graphs: a graph is undergoing both edge insertions and deletions, and the goal is to efficiently maintain a large matching after each edge update. This problem has received considerable attention in recent years. The known algorithms naturally exhibit a trade-off between the quality of the matching maintained (i.e., the approximation ratio) and the time needed per update. While several interesting results have been obtained, the optimal behavior of this trade-off remains largely unclear. Our main contribution is a new approach to designing fully dynamic approximate matching algorithms that in a unified manner not only (essentially) recovers all previously known trade-offs that were achieved via very different techniques, but reveals some new ones as well. As our main tool to achieve this, we introduce a generalization of the edge-degree constrained subgraph (EDCS) of Bernstein and Stein (2015) that we call the hierarchical EDCS (HEDCS).