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Maximum Matching in the Online Batch-arrival Model

Authors:

Sahil SinglaAuthors Info & Claims

ACM Transactions on Algorithms (TALG), Volume 16, Issue 4

Article No.: 49, Pages 1 - 31

https://doi.org/10.1145/3399676

Published: 20 July 2020 Publication History

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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, i.e., it 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 ratio ½ + 2−^O(s).

Our algorithms use a novel Instance-Optimal-LP and combine graph decomposition techniques with online primal-dual analysis.

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Cited By

Bampis EEscoffier BYoussef PAgmon NAn BRicci AYeoh W(2023)Online 2-stage Stable MatchingProceedings of the 2023 International Conference on Autonomous Agents and Multiagent Systems10.5555/3545946.3598972(2475-2477)Online publication date: 30-May-2023
https://dl.acm.org/doi/10.5555/3545946.3598972
Bampis EEscoffier BYoussef P(2023)Online 2-stage stable matchingDiscrete Applied Mathematics10.1016/j.dam.2023.09.009341:C(394-405)Online publication date: 31-Dec-2023
https://dl.acm.org/doi/10.1016/j.dam.2023.09.009
Eshghali MKrokhmal P(2023)Risk‐averse optimization and resilient network flowsNetworks10.1002/net.2214982:2(129-152)Online publication date: 13-May-2023
https://doi.org/10.1002/net.22149

Index Terms

Maximum Matching in the Online Batch-arrival Model
1. Mathematics of computing
  1. Discrete mathematics
    1. Graph theory
      1. Approximation algorithms
      2. Matchings and factors
2. Theory of computation
  1. Design and analysis of algorithms
    1. Online algorithms

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Published In

cover image ACM Transactions on Algorithms

ACM Transactions on Algorithms Volume 16, Issue 4

October 2020

404 pages

ISSN:1549-6325

EISSN:1549-6333

DOI:10.1145/3407674

Editor:
Aravind Srinivasan
University of Maryland, USA

Issue’s Table of Contents

Copyright © 2020 ACM.

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Association for Computing Machinery

New York, NY, United States

Publication History

Published: 20 July 2020

Accepted: 01 May 2020

Revised: 01 January 2020

Received: 01 January 2019

Published in TALG Volume 16, Issue 4

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Cited By

Bampis EEscoffier BYoussef PAgmon NAn BRicci AYeoh W(2023)Online 2-stage Stable MatchingProceedings of the 2023 International Conference on Autonomous Agents and Multiagent Systems10.5555/3545946.3598972(2475-2477)Online publication date: 30-May-2023
https://dl.acm.org/doi/10.5555/3545946.3598972
Bampis EEscoffier BYoussef P(2023)Online 2-stage stable matchingDiscrete Applied Mathematics10.1016/j.dam.2023.09.009341:C(394-405)Online publication date: 31-Dec-2023
https://dl.acm.org/doi/10.1016/j.dam.2023.09.009
Eshghali MKrokhmal P(2023)Risk‐averse optimization and resilient network flowsNetworks10.1002/net.2214982:2(129-152)Online publication date: 13-May-2023
https://doi.org/10.1002/net.22149

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