An improved approximation ratio for the minimum latency problem
Proceedings of the seventh annual ACM-SIAM symposium on Discrete algorithms
Competitive analysis of incentive compatible on-line auctions
Proceedings of the 2nd ACM conference on Electronic commerce
Reducing truth-telling online mechanisms to online optimization
Proceedings of the thirty-fifth annual ACM symposium on Theory of computing
Greedy facility location algorithms analyzed using dual fitting with factor-revealing LP
Journal of the ACM (JACM)
Adaptive limited-supply online auctions
EC '04 Proceedings of the 5th ACM conference on Electronic commerce
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
AdWords and generalized online matching
Journal of the ACM (JACM)
Online auctions and generalized secretary problems
ACM SIGecom Exchanges
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
Secretary problems: weights and discounts
SODA '09 Proceedings of the twentieth Annual ACM-SIAM Symposium on Discrete Algorithms
Algorithms for Secretary Problems on Graphs and Hypergraphs
ICALP '09 Proceedings of the 36th Internatilonal Collogquium on Automata, Languages and Programming: Part II
Online primal-dual algorithms for maximizing ad-auctions revenue
ESA'07 Proceedings of the 15th annual European conference on Algorithms
Incentives in online auctions via linear programming
WINE'10 Proceedings of the 6th international conference on Internet and network economics
Hiring a secretary from a poset
Proceedings of the 12th ACM conference on Electronic commerce
Improved competitive ratios for submodular secretary problems
APPROX'11/RANDOM'11 Proceedings of the 14th international workshop and 15th international conference on Approximation, randomization, and combinatorial optimization: algorithms and techniques
On variants of the matroid secretary problem
ESA'11 Proceedings of the 19th European conference on Algorithms
Matroid secretary problem in the random assignment model
Proceedings of the twenty-second annual ACM-SIAM symposium on Discrete Algorithms
Interviewing secretaries in parallel
Proceedings of the 13th ACM Conference on Electronic Commerce
Hi-index | 0.00 |
In the classical secretary problem an employer would like to choose the best candidate among n competing candidates that arrive in a random order. This basic concept of n elements arriving in a random order and irrevocable decisions made by an algorithm have been explored extensively over the years, and used for modeling the behavior of many processes. Our main contribution is a new linear programming technique that we introduce as a tool for obtaining and analyzing mechanisms for the secretary problem and its variants. The linear program is formulated using judiciously chosen variables and constraints and we show a one-to-one correspondence between mechanisms for the secretary problem and feasible solutions to the linear program. Capturing the set of mechanisms as a linear polytope holds the following immediate advantages. Computing the optimal mechanism reduces to solving a linear program. Proving an upper bound on the performance of any mechanism reduces to finding a feasible solution to the dual program. Exploring variants of the problem is as simple as adding new constraints, or manipulating the objective function of the linear program. We demonstrate these ideas by exploring some natural variants of the secretary problem. In particular, using our approach, we design optimal secretary mechanisms in which the probability of selecting a candidate at any position is equal. We refer to such mechanisms as incentive compatible and these mechanisms are motivated by the recent applications of secretary problems to online auctions. We also show a family of linear programs which characterize all mechanisms that are allowed to choose J candidates and gain profit from the K best candidates. We believe that linear programming based approach may be very helpful in the context of other variants of the secretary problem.