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
Competitive Weighted Matching in Transversal Matroids
ICALP '08 Proceedings of the 35th international colloquium on Automata, Languages and Programming, Part I
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
Automated online mechanism design and prophet inequalities
AAAI'07 Proceedings of the 22nd national conference on Artificial intelligence - Volume 1
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
Constrained non-monotone submodular maximization: offline and secretary algorithms
WINE'10 Proceedings of the 6th international conference on Internet and network economics
Secretary problems: laminar matroid and interval scheduling
Proceedings of the twenty-second 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
Secretary problems via linear programming
IPCO'10 Proceedings of the 14th international conference on Integer Programming and Combinatorial Optimization
STOC '12 Proceedings of the forty-fourth annual ACM symposium on Theory of computing
Advances on matroid secretary problems: free order model and laminar case
IPCO'13 Proceedings of the 16th international conference on Integer Programming and Combinatorial Optimization
Recent advances on the matroid secretary problem
ACM SIGACT News
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We present a number of positive and negative results for variants of the matroid secretary problem. Most notably, we design a constant-factor competitive algorithm for the "random assignment" model where the weights are assigned randomly to the elements of a matroid, and then the elements arrive on-line in an adversarial order (extending a result of Soto [20]). This is under the assumption that the matroid is known in advance. If the matroid is unknown in advance, we present an O(log r log n)-approximation, and prove that a better than O(log n/ log log n) approximation is impossible. This resolves an open question posed by Babaioff et al. [3]. As a natural special case, we also consider the classical secretary problem where the number of candidates n is unknown in advance. If n is chosen by an adversary from {1,...,N}, we provide a nearly tight answer, by providing an algorithm that chooses the best candidate with probability at least 1/(HN-1 + 1) and prove that a probability better than 1/HN cannot be achieved (where HN is the N-th harmonic number).