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
Online auctions and generalized secretary problems
ACM SIGecom Exchanges
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
Algorithms for Secretary Problems on Graphs and Hypergraphs
ICALP '09 Proceedings of the 36th Internatilonal Collogquium on Automata, Languages and Programming: Part II
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
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
STOC '12 Proceedings of the forty-fourth annual ACM symposium on Theory of computing
Secretary problems with convex costs
ICALP'12 Proceedings of the 39th international colloquium conference on Automata, Languages, and Programming - Volume Part I
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
Stochastic combinatorial optimization via poisson approximation
Proceedings of the forty-fifth annual ACM symposium on Theory of computing
Recent advances on the matroid secretary problem
ACM SIGACT News
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The Matroid Secretary Problem, introduced by Babaioff et al. (2007), is a generalization of the Classical Secretary Problem. In this problem, elements from a matroid are presented to an on-line algorithm in a random order. Each element has a weight associated with it, which is revealed to the algorithm along with the element. After each element is revealed the algorithm must make an irrevocable decision on whether or not to select it. The goal is to pick an independent set with the sum of the weights of the selected elements as large as possible. Babaioff et al gave an algorithm for the Matroid Secretary Problem with a competitive ratio of O(logρ), where ρ is the rank of the matroid. It has been conjectured that a constant competitive-ratio is achievable for this problem. In this paper we give an algorithm that has a competitive-ratio of O(√logρ).