# Online minimum matching with uniform metric and random arrivals

```@article{Duppala2022OnlineMM,
title={Online minimum matching with uniform metric and random arrivals},
author={Sharmila Duppala and Karthik Abinav Sankararaman and Pan Xu},
journal={Oper. Res. Lett.},
year={2022},
volume={50},
pages={45-49}
}```
• Published 9 December 2021
• Computer Science, Mathematics
• Oper. Res. Lett.

## References

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Randomized online algorithms for minimum metric bipartite matching
• Computer Science, Mathematics
SODA '06
• 2006
This work shows that a simple randomized greedy algorithm is competitive on a hierarchically separated tree and presents the first poly-logarithmic competitive online algorithm for minimum metric bipartite matching.
Stochastic Online Metric Matching
• Computer Science, Mathematics
ICALP
• 2019
The main result is an \$O((\log \log n)^2)\$-competitive algorithm in this model, which implies a strict separation between the i.i.d model and the adversarial and random order models, both for general metrics and these much-studied metrics.
Online Weighted Matching
• Computer Science
J. Algorithms
• 1993
A simple 2 k − 1 competitive algorithm for online minimum weighted bipartite matching where 2 k is the number of nodes is presented and it is shown that this competitiveness is optimal.
A Randomized O(log2k)-Competitive Algorithm for Metric Bipartite Matching
• Mathematics, Computer Science
Algorithmica
• 2012
An O(log2k)-competitive randomized algorithm is given for the online metric matching problem, which improves upon the best known guarantee of O( log3k) on the competitive factor due to Meyerson, Nanavati and Poplawski.
Matching on the Line Admits No o(√log n)-Competitive Algorithm
• Computer Science
ICALP
• 2021
We present a simple proof that the competitive ratio of any randomized online matching algorithm for the line exceeds √ log2(n+1)/15 for all n = 2−1 : i ∈ N, settling a 25-year-old open question.
A Robust and Optimal Online Algorithm for Minimum Metric Bipartite Matching
This work presents a deterministic online algorithm that is the first to simultaneously achieve optimal performances in the well-known adversarial and the random arrival models and proves that any online algorithm will have a competitive ratio of at least 2H_n - 1-o(1) in this model.
Optimal Analysis of an Online Algorithm for the Bipartite Matching Problem on a Line
The analysis of the deterministic Robust Matching Algorithm is improved and it is shown that WFA cannot achieve an asymptotically better competitive ratio than the RM-Algorithm.