@inproceedings{78b686843edd4d449fc4ac68e9f417de,
title = "Maximum matching in the online batch-arrival model",
abstract = "Consider a two-stage matching problem, where edges of an input graph are revealed in two stages (batches) and in each stage we have to immediately and irrevocably extend our matching using the edges from that stage. The natural greedy algorithm is half competitive. Even though there is a huge literature on online matching in adversarial vertex arrival model, no positive results were previously known in adversarial edge arrival model. For two-stage bipartite matching problem, we show that the optimal competitive ratio is exactly 2/3 in both the fractional and the randomized-integral models. Furthermore, our algorithm for fractional bipartite matching is instance optimal—achieves the best competitive ratio for any given first stage graph. We also study natural extensions of this problem to general graphs and to s stages, and present randomized-integral algorithms with competitive ratio12 +2−O(s). Our algorithms use a novel LP and combine graph decomposition techniques with online primal-dual analysis.",
keywords = "Competitive ratio, Edmonds-Gallai decomposition, Matching, Online algorithms, Primal-dual analysis, Semi-streaming",
author = "Euiwoong Lee and Sahil Singla",
note = "Publisher Copyright: {\textcopyright} Springer International Publishing AG 2017.; 19th International Conference on Integer Programming and Combinatorial Optimization, IPCO 2017 ; Conference date: 26-06-2017 Through 28-06-2017",
year = "2017",
doi = "10.1007/978-3-319-59250-3_29",
language = "English (US)",
isbn = "9783319592497",
series = "Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)",
publisher = "Springer Verlag",
pages = "355--367",
editor = "Friedrich Eisenbrand and Jochen Koenemann",
booktitle = "Integer Programming and Combinatorial Optimization - 19th International Conference, IPCO 2017, Proceedings",
address = "Germany",
}