Optimal Competitive Ratio of Two-sided Online Bipartite Matching
Zhihao Gavin Tang
TL;DR
This paper proves the best possible competitive ratio of approximately 0.526 for the fractional two-sided online bipartite matching problem, confirming the optimality of previous bounds.
Contribution
It establishes an exact upper bound on the competitive ratio, matching the known lower bounds, thus resolving the optimality question for this problem.
Findings
Optimal competitive ratio is approximately 0.526.
The bound matches previous lower bounds, confirming optimality.
The result applies to fractional online bipartite matching with two-sided arrivals.
Abstract
We establish an optimal upper bound (negative result) of on the competitive ratio of the fractional version of online bipartite matching with two-sided vertex arrivals, matching the lower bound (positive result) achieved by Wang and Wong (ICALP 2015), and Tang and Zhang (EC 2024).
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Taxonomy
TopicsOptimization and Search Problems · Advanced Bandit Algorithms Research · Complexity and Algorithms in Graphs