research-article

Online stochastic matching: online actions based on offline statistics

Authors:

Vahideh H. Manshadi,

Shayan Oveis Gharan,

Amin SaberiAuthors Info & Claims

SODA '11: Proceedings of the twenty-second annual ACM-SIAM symposium on Discrete algorithms

Pages 1285 - 1294

Published: 23 January 2011 Publication History

Get Access

Abstract

We consider the online stochastic matching problem proposed by Feldman et al. [4] as a model of display ad allocation. We are given a bipartite graph; one side of the graph corresponds to a fixed set of bins and the other side represents the set of possible ball types. At each time step, a ball is sampled independently from the given distribution and it needs to be matched upon its arrival to an empty bin. The goal is to maximize the size of the matching.

We present an online algorithm for this problem with a competitive ratio of 0.702. Before our result, algorithms with a competitive ratio better than 1−1/e were known under the assumption that the expected number of arriving balls of each type is integral. A key idea of the algorithm is to collect statistics about the decisions of the optimum offline solution using Monte Carlo sampling and use those statistics to guide the decisions of the online algorithm. We also show that no online algorithm can have a competitive ratio better than 0.823.

References

[1]

B. Bahmani and M. Kapralov. Improved bounds for online stochastic matching. In ESA, pages 170--181, 2010.

Digital Library

Google Scholar

[2]

N. R. Devanur and T. P. Hayes. The adwords problem: online keyword matching with budgeted bidders under random permutations. In EC, pages 71--78, 2009.

Digital Library

Google Scholar

[3]

M. Dietzfelbinger, A. Goerdt, M. Mitzenmacher, A. Montanari, R. Pagh, and M. Rink. Tight thresholds for cuckoo hashing via xorsat. SIAM Journal on Computing, 2009.

Google Scholar

[4]

J. Feldman, A. Mehta, V. S. Mirrokni, and S. Muthukrishnan. Online stochastic matching: Beating 1-1/e. In FOCS, pages 117--126, 2009.

Digital Library

Google Scholar

[5]

N. Fountoulakis and K. Panagiotou. Sharp load thresholds for cuckoo hashing. arXiv, cs.DS, Jan. 2009.

Google Scholar

[6]

A. Frieze and P. Melsted. Maximum matchings in random bipartite graphs and the space utilization of cuckoo hashtables. arxiv report 0910.5535v3, 2009.

Google Scholar

[7]

G. Goel and A. Mehta. Online budgeted matching in random input models with applications to adwords. In SODA, pages 982--991, 2008.

Digital Library

Google Scholar

[8]

R. M. Karp, U. V. Vazirani, and V. V. Vazirani. An optimal algorithm for on-line bipartite matching. In STOC, pages 352--358. ACM, 1990.

Digital Library

Google Scholar

[9]

A. Mehta, A. Saberi, U. Vazirani, and V. Vazirani. Adwords and generalized online matching. J. ACM, 54(5):22, 2007.

Digital Library

Google Scholar

[10]

R. Pagh and F. F. Rodler. Cuckoo hashing. J. Algorithms, 51(2):122--144, 2004.

Digital Library

Google Scholar

Cited By

View all

Gamlath BKale SSvensso OChan T(2019)Beating greedy for stochastic bipartite matchingProceedings of the Thirtieth Annual ACM-SIAM Symposium on Discrete Algorithms10.5555/3310435.3310611(2841-2854)Online publication date: 6-Jan-2019
https://dl.acm.org/doi/10.5555/3310435.3310611
Gravin NWang HKarlin AImmorlica NJohari R(2019)Prophet Inequality for Bipartite MatchingProceedings of the 2019 ACM Conference on Economics and Computation10.1145/3328526.3329604(93-109)Online publication date: 17-Jun-2019
https://dl.acm.org/doi/10.1145/3328526.3329604
Ashlagi IBurq MDutta CJaillet PSaberi ASholley CKarlin AImmorlica NJohari R(2019)Edge Weighted Online Windowed MatchingProceedings of the 2019 ACM Conference on Economics and Computation10.1145/3328526.3329573(729-742)Online publication date: 17-Jun-2019
https://dl.acm.org/doi/10.1145/3328526.3329573
Show More Cited By

Online stochastic matching: online actions based on offline statistics

Recommendations

Online Matching with Stochastic Rewards
FOCS '12: Proceedings of the 2012 IEEE 53rd Annual Symposium on Foundations of Computer Science

The online matching problem has received significant attention in recent years because of its connections to allocation problems in Internet advertising, crowd-sourcing, etc. In these real-world applications, the typical goal is not to maximize the ...
Online Stochastic Matching: Online Actions Based on Offline Statistics

We consider the online stochastic matching problem proposed by Feldman et al. [Feldman J, Mehta A, Mirrokni VS, Muthukrishnan S (2009) Online stochastic matching: Beating 1-1/e. Annual IEEE Sympos. Foundations Comput. Sci. 117--126] as a model of ...
Online Matching with Stochastic Rewards: Optimal Competitive Ratio via Path-Based Formulation
In the paper “Online Matching with Stochastic Rewards: Optimal Competitive Ratio via Path-Based Formulation,” the authors develop a novel algorithm analysis approach to address stochastic elements in online matching. The approach leads to several new ...
The problem of online matching with stochastic rewards is a generalization of the online bipartite matching problem where each edge has a probability of success. When a match is made it succeeds with the probability of the corresponding edge. We consider ...

Comments

Information & Contributors

Information

Published In

SODA '11: Proceedings of the twenty-second annual ACM-SIAM symposium on Discrete algorithms

January 2011

1785 pages

Program Chair:
Dana Randall
Georgia Institute of Technology

Publisher

Society for Industrial and Applied Mathematics

United States

Publication History

Published: 23 January 2011

Check for updates

Qualifiers

Research-article

Conference

SODA '11

Sponsor:

SIGACT

SODA '11: 22nd ACM-SIAM Symposium on Discrete Algorithms

January 23 - 25, 2011

California, San Francisco

Acceptance Rates

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

Contributors

Other Metrics

View Article Metrics

Bibliometrics & Citations

Bibliometrics

Article Metrics

25
Total Citations
View Citations
114
Total Downloads

Downloads (Last 12 months)1
Downloads (Last 6 weeks)0

Reflects downloads up to 15 Jan 2025

Other Metrics

View Author Metrics

Citations

Cited By

View all

Gamlath BKale SSvensso OChan T(2019)Beating greedy for stochastic bipartite matchingProceedings of the Thirtieth Annual ACM-SIAM Symposium on Discrete Algorithms10.5555/3310435.3310611(2841-2854)Online publication date: 6-Jan-2019
https://dl.acm.org/doi/10.5555/3310435.3310611
Gravin NWang HKarlin AImmorlica NJohari R(2019)Prophet Inequality for Bipartite MatchingProceedings of the 2019 ACM Conference on Economics and Computation10.1145/3328526.3329604(93-109)Online publication date: 17-Jun-2019
https://dl.acm.org/doi/10.1145/3328526.3329604
Ashlagi IBurq MDutta CJaillet PSaberi ASholley CKarlin AImmorlica NJohari R(2019)Edge Weighted Online Windowed MatchingProceedings of the 2019 ACM Conference on Economics and Computation10.1145/3328526.3329573(729-742)Online publication date: 17-Jun-2019
https://dl.acm.org/doi/10.1145/3328526.3329573
Esfandiari HKorula NMirrokni V(2018)Allocation with Traffic SpikesACM Transactions on Economics and Computation10.1145/31054466:3-4(1-23)Online publication date: 23-Oct-2018
https://dl.acm.org/doi/10.1145/3105446
Wang YWong SConitzer VBergemann DChen Y(2016)Matroid Online Bipartite Matching and Vertex CoverProceedings of the 2016 ACM Conference on Economics and Computation10.1145/2940716.2940793(437-454)Online publication date: 21-Jul-2016
https://dl.acm.org/doi/10.1145/2940716.2940793
Devanur NHuang ZKorula NMirrokni VYan Q(2016)Whole-Page Optimization and Submodular Welfare Maximization with Online BiddersACM Transactions on Economics and Computation10.1145/28925634:3(1-20)Online publication date: 6-Apr-2016
https://dl.acm.org/doi/10.1145/2892563
Agrawal SDevanur NIndyk P(2015)Fast algorithms for online stochastic convex programmingProceedings of the twenty-sixth annual ACM-SIAM symposium on Discrete algorithms10.5555/2722129.2722222(1405-1424)Online publication date: 4-Jan-2015
https://dl.acm.org/doi/10.5555/2722129.2722222
Mehta AWaggoner BZadimoghaddam MIndyk P(2015)Online stochastic matching with unequal probabilitiesProceedings of the twenty-sixth annual ACM-SIAM symposium on Discrete algorithms10.5555/2722129.2722221(1388-1404)Online publication date: 4-Jan-2015
https://dl.acm.org/doi/10.5555/2722129.2722221
Esfandiari HKorula NMirrokni VRoughgarden TFeldman MSchwarz M(2015)Online Allocation with Traffic SpikesProceedings of the Sixteenth ACM Conference on Economics and Computation10.1145/2764468.2764536(169-186)Online publication date: 15-Jun-2015
https://dl.acm.org/doi/10.1145/2764468.2764536
Korula NMirrokni VZadimoghaddam MServedio RRubinfeld R(2015)Online Submodular Welfare MaximizationProceedings of the forty-seventh annual ACM symposium on Theory of Computing10.1145/2746539.2746626(889-898)Online publication date: 14-Jun-2015
https://dl.acm.org/doi/10.1145/2746539.2746626
Show More Cited By

View Options

Login options

Check if you have access through your login credentials or your institution to get full access on this article.

Cited By

Recommendations

Online Matching with Stochastic Rewards