Improved Algorithms and Analysis for Secretary Problems and Generalizations
SIAM Journal on Discrete Mathematics
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
Maximizing Non-Monotone Submodular Functions
FOCS '07 Proceedings of the 48th Annual IEEE Symposium on Foundations of Computer Science
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
Maximizing submodular set functions subject to multiple linear constraints
SODA '09 Proceedings of the twentieth Annual ACM-SIAM Symposium on Discrete Algorithms
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
Submodular Maximization over Multiple Matroids via Generalized Exchange Properties
APPROX '09 / RANDOM '09 Proceedings of the 12th International Workshop and 13th International Workshop on Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques
On Maximizing Welfare When Utility Functions Are Subadditive
SIAM Journal on Computing
Symmetry and Approximability of Submodular Maximization Problems
FOCS '09 Proceedings of the 2009 50th Annual IEEE Symposium on Foundations of Computer Science
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
Maximizing Nonmonotone Submodular Functions under Matroid or Knapsack Constraints
SIAM Journal on Discrete Mathematics
Constrained non-monotone submodular maximization: offline and secretary algorithms
WINE'10 Proceedings of the 6th international conference on Internet and network economics
Submodular function maximization via the multilinear relaxation and contention resolution schemes
Proceedings of the forty-third annual ACM symposium on Theory of computing
Submodular maximization by simulated annealing
Proceedings of the twenty-second 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
Secretary problems via linear programming
IPCO'10 Proceedings of the 14th international conference on Integer Programming and Combinatorial Optimization
Maximizing a Monotone Submodular Function Subject to a Matroid Constraint
SIAM Journal on Computing
Learning on a budget: posted price mechanisms for online procurement
Proceedings of the 13th ACM Conference on Electronic Commerce
Interviewing secretaries in parallel
Proceedings of the 13th ACM Conference on Electronic Commerce
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
Recent advances on the matroid secretary problem
ACM SIGACT News
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The Classical Secretary Problem was introduced during the 60's of the 20th century, nobody is sure exactly when. Since its introduction, many variants of the problem have been proposed and researched. In the classical secretary problem, and many of its variant, the input (which is a set of secretaries, or elements) arrives in a random order. In this paper we apply to the secretary problem a simple observation which states that the random order of the input can be generated by independently choosing a random continuous arrival time for each secretary. Surprisingly, this simple observation enables us to improve the competitive ratio of several known and studied variants of the secretary problem. In addition, in some cases the proofs we provide assuming random arrival times are shorter and simpler in comparison to existing proofs. In this work we consider three variants of the secretary problem, all of which have the same objective of maximizing the value of the chosen set of secretaries given a monotone submodular function f. In the first variant we are allowed to hire a set of secretaries only if it is an independent set of a given partition matroid. The second variant allows us to choose any set of up to k secretaries. In the last and third variant, we can hire any set of secretaries satisfying a given knapsack constraint.