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
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
Constrained non-monotone submodular maximization: offline and secretary algorithms
WINE'10 Proceedings of the 6th international conference on Internet and network economics
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
Improved competitive ratio for the matroid secretary problem
Proceedings of the twenty-third annual ACM-SIAM symposium on Discrete Algorithms
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
Recent advances on the matroid secretary problem
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The best-known conjecture in the context of matroid secretary problems claims the existence of an O(1)-approximation applicable to any matroid. Whereas this conjecture remains open, modified forms of it were shown to be true, when assuming that the assignment of weights to the secretaries is not adversarial but uniformly at random [20,18]. However, so far, no variant of the matroid secretary problem with adversarial weight assignment is known that admits an O(1)-approximation. We address this point by presenting a 9-approximation for the free order model, a model suggested shortly after the introduction of the matroid secretary problem, and for which no O(1)-approximation was known so far. The free order model is a relaxed version of the original matroid secretary problem, with the only difference that one can choose the order in which secretaries are interviewed. Furthermore, we consider the classical matroid secretary problem for the special case of laminar matroids. Only recently, a O(1)-approximation has been found for this case, using a clever but rather involved method and analysis [12] that leads to a 16000/3-approximation. This is arguably the most involved special case of the matroid secretary problem for which an O(1)-approximation is known. We present a considerably simpler and stronger $3\sqrt{3}e\approx 14.12$-approximation, based on reducing the problem to a matroid secretary problem on a partition matroid.