research-article

Randomized primal-dual analysis of RANKING for online bipartite matching

Authors:

Nikhil R. Devanur,

Kamal Jain,

Robert D. KleinbergAuthors Info & Claims

SODA '13: Proceedings of the twenty-fourth annual ACM-SIAM symposium on Discrete algorithms

Pages 101 - 107

Published: 06 January 2013 Publication History

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Abstract

We give a simple proof that the ranking algorithm of Karp, Vazirani and Vazirani [KVV90] is 1-1/e competitive for the online bipartite matching problem. The proof is via a randomized primal-dual argument. Primal-dual algorithms have been successfully used for many online algorithm problems, but the dual constraints are always satisfied deterministically. This is the first instance of a non-trivial randomized primal-dual algorithm in which the dual constraints only hold in expectation. The approach also generalizes easily to the vertex-weighted version considered by Agarwal et al. [AGKM11]. Further we show that the proof is very similar to the deterministic primal-dual argument for the online budgeted allocation problem with small bids (also called the AdWords problem) of Mehta et al. [MSVV05].

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{KVV90} R. M. Karp, U. V. Vazirani, and V. V. Vazirani. An optimal algorithm for on-line bipartite matching. In STOC '90: Proceedings of the twenty-second annual ACM symposium on Theory of computing, pages 352--358, 1990.

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{MSVV05} Aranyak Mehta, Amin Saberi, Umesh Vazirani, and Vijay Vazirani. Adwords and generalized on-line matching. In In FOCS 05: Proceedings of the 46th Annual IEEE Symposium on Foundations of Computer Science, pages 264--273. IEEE Computer Society, 2005.

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Amouzandeh ASchmitt Svan Stee R(2024)SIGACT News Online Algorithms Column 41: 2023 in reviewACM SIGACT News10.1145/3639528.363953854:4(108-125)Online publication date: 3-Jan-2024
https://dl.acm.org/doi/10.1145/3639528.3639538
Li PYang JRen SKrause ABrunskill ECho KEngelhardt BSabato SScarlett J(2023)Learning for edge-weighted online bipartite matching with robustness guaranteesProceedings of the 40th International Conference on Machine Learning10.5555/3618408.3619244(20276-20295)Online publication date: 23-Jul-2023
https://dl.acm.org/doi/10.5555/3618408.3619244
Bienkowski MFuchssteiner DSchmid SMohror KArnold DBadia R(2023)Optimizing Reconfigurable Optical Datacenters: The Power of RandomizationProceedings of the International Conference for High Performance Computing, Networking, Storage and Analysis10.1145/3581784.3607057(1-11)Online publication date: 12-Nov-2023
https://dl.acm.org/doi/10.1145/3581784.3607057
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Index Terms

Randomized primal-dual analysis of RANKING for online bipartite matching
1. Mathematics of computing
  1. Discrete mathematics
    1. Graph theory
      1. Graph algorithms
      2. Graph enumeration
2. Theory of computation

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Published In

SODA '13: Proceedings of the twenty-fourth annual ACM-SIAM symposium on Discrete algorithms

January 2013

1935 pages

ISBN:9781611972511

Program Chair:
Sanjeev Khanna
University of Pennsylvania

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SIGACT: ACM Special Interest Group on Algorithms and Computation Theory

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Society for Industrial and Applied Mathematics

United States

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Published: 06 January 2013

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SODA '13

SODA '13: ACM-SIAM Symposium on Discrete Algorithms

January 6 - 8, 2013

Louisiana, New Orleans

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Overall Acceptance Rate 411 of 1,322 submissions, 31%

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Amouzandeh ASchmitt Svan Stee R(2024)SIGACT News Online Algorithms Column 41: 2023 in reviewACM SIGACT News10.1145/3639528.363953854:4(108-125)Online publication date: 3-Jan-2024
https://dl.acm.org/doi/10.1145/3639528.3639538
Li PYang JRen SKrause ABrunskill ECho KEngelhardt BSabato SScarlett J(2023)Learning for edge-weighted online bipartite matching with robustness guaranteesProceedings of the 40th International Conference on Machine Learning10.5555/3618408.3619244(20276-20295)Online publication date: 23-Jul-2023
https://dl.acm.org/doi/10.5555/3618408.3619244
Bienkowski MFuchssteiner DSchmid SMohror KArnold DBadia R(2023)Optimizing Reconfigurable Optical Datacenters: The Power of RandomizationProceedings of the International Conference for High Performance Computing, Networking, Storage and Analysis10.1145/3581784.3607057(1-11)Online publication date: 12-Nov-2023
https://dl.acm.org/doi/10.1145/3581784.3607057
Fahrbach MHuang ZTao RZadimoghaddam M(2022)Edge-Weighted Online Bipartite MatchingJournal of the ACM10.1145/355697169:6(1-35)Online publication date: 17-Nov-2022
https://dl.acm.org/doi/10.1145/3556971
Feng YNiazadeh RSaberi AMarx D(2021)Two-stage stochastic matching with application to ride hailingProceedings of the Thirty-Second Annual ACM-SIAM Symposium on Discrete Algorithms10.5555/3458064.3458234(2862-2877)Online publication date: 10-Jan-2021
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Levin RWajc DMarx D(2021)Streaming submodular matching meets the primal-dual methodProceedings of the Thirty-Second Annual ACM-SIAM Symposium on Discrete Algorithms10.5555/3458064.3458178(1914-1933)Online publication date: 10-Jan-2021
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