Stochastic on-line knapsack problems
Mathematical Programming: Series A and B
Online computation and competitive analysis
Online computation and competitive analysis
Average-case analysis of off-line and on-line knapsack problems
Proceedings of the sixth annual ACM-SIAM symposium on Discrete algorithms
Competitive auctions and digital goods
SODA '01 Proceedings of the twelfth annual ACM-SIAM symposium on Discrete algorithms
The Dynamic and Stochastic Knapsack Problem
Operations Research
FOCS '01 Proceedings of the 42nd IEEE symposium on Foundations of Computer Science
Adaptive limited-supply online auctions
EC '04 Proceedings of the 5th ACM conference on Electronic commerce
Smoothed analysis of algorithms: Why the simplex algorithm usually takes polynomial time
Journal of the ACM (JACM)
Approximating the Stochastic Knapsack Problem: The Benefit of Adaptivity
FOCS '04 Proceedings of the 45th Annual IEEE Symposium on Foundations of Computer Science
A multiple-choice secretary algorithm with applications to online auctions
SODA '05 Proceedings of the sixteenth annual ACM-SIAM symposium on Discrete algorithms
Matroids, secretary problems, and online mechanisms
SODA '07 Proceedings of the eighteenth annual ACM-SIAM symposium on Discrete algorithms
Competitive Weighted Matching in Transversal Matroids
ICALP '08 Proceedings of the 35th international colloquium on Automata, Languages and Programming, Part I
A Knapsack Secretary Problem with Applications
APPROX '07/RANDOM '07 Proceedings of the 10th International Workshop on Approximation and the 11th International Workshop on Randomization, and Combinatorial Optimization. Algorithms and Techniques
Online primal-dual algorithms for covering and packing problems
ESA'05 Proceedings of the 13th annual European conference on Algorithms
The Secretary Problem with a Hazard Rate Condition
WINE '08 Proceedings of the 4th International Workshop on Internet and Network Economics
Optimal Algorithms for the Online Time Series Search Problem
COCOA '09 Proceedings of the 3rd International Conference on Combinatorial Optimization and Applications
Online network design with outliers
ICALP'10 Proceedings of the 37th international colloquium conference on Automata, languages and programming
Submodular secretary problem and extensions
APPROX/RANDOM'10 Proceedings of the 13th international conference on Approximation, and 14 the International conference on Randomization, and combinatorial optimization: algorithms and techniques
Online stochastic packing applied to display ad allocation
ESA'10 Proceedings of the 18th annual European conference on Algorithms: Part I
Optimal algorithms for the online time series search problem
Theoretical Computer Science
Incentives in online auctions via linear programming
WINE'10 Proceedings of the 6th international conference on Internet and network economics
On the competitive ratio of online sampling auctions
WINE'10 Proceedings of the 6th international conference on Internet and network economics
Secretary problems and incentives via linear programming
ACM SIGecom Exchanges
Hiring a secretary from a poset
Proceedings of the 12th ACM conference on Electronic commerce
Online algorithms for the multiple time series search problem
Computers and Operations Research
Improved competitive ratio for the matroid secretary problem
Proceedings of the twenty-third annual ACM-SIAM symposium on Discrete Algorithms
Matroid secretary problem in the random assignment model
Proceedings of the twenty-second annual ACM-SIAM symposium on Discrete Algorithms
Optimal algorithms for online time series search and one-way trading with interrelated prices
Journal of Combinatorial Optimization
Secretary problems via linear programming
IPCO'10 Proceedings of the 14th international conference on Integer Programming and Combinatorial Optimization
Geometry of online packing linear programs
ICALP'12 Proceedings of the 39th international colloquium conference on Automata, Languages, and Programming - Volume Part I
Competitive analysis of maintaining frequent items of a stream
SWAT'12 Proceedings of the 13th Scandinavian conference on Algorithm Theory
Limited supply online auctions for revenue maximization
WINE'12 Proceedings of the 8th international conference on Internet and Network Economics
On the Competitive Ratio of Online Sampling Auctions
ACM Transactions on Economics and Computation - Special Issue on Algorithmic Game Theory
How much is it worth to know the future in online conversion problems?
Discrete Applied Mathematics
Pricing mechanisms for crowdsourcing markets
Proceedings of the 22nd international conference on World Wide Web
Recent advances on the matroid secretary problem
ACM SIGACT News
Submodular secretary problem and extensions
ACM Transactions on Algorithms (TALG)
Real time bid optimization with smooth budget delivery in online advertising
Proceedings of the Seventh International Workshop on Data Mining for Online Advertising
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We present generalized secretary problems as a framework for online auctions. Elements, such as potential employees or customers, arrive one by one online. After observing the value derived from an element, but without knowing the values of future elements, the algorithm has to make an irrevocable decision whether to retain the element as part of a solution, or reject it. The way in which the secretary framework differs from traditional online algorithms is that the elements arrive in uniformly random order. Many natural online auction scenarios can be cast as generalized secretary problems, by imposing natural restrictions on the feasible sets. For many such settings, we present surprisingly strong constant factor guarantees on the expected value of solutions obtained by online algorithms. The framework is also easily augmented to take into account time-discounted revenue and incentive compatibility. We give an overview of recent results and future research directions.