Randomized algorithms
Competitive generalized auctions
STOC '02 Proceedings of the thiry-fourth annual ACM symposium on Theory of computing
Truth revelation in approximately efficient combinatorial auctions
Journal of the ACM (JACM)
Truthful approximation mechanisms for restricted combinatorial auctions: extended abstract
Eighteenth national conference on Artificial intelligence
Adaptive limited-supply online auctions
EC '04 Proceedings of the 5th ACM conference on Electronic commerce
From optimal limited to unlimited supply auctions
Proceedings of the 6th 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
Online ascending auctions for gradually expiring items
SODA '05 Proceedings of the sixteenth annual ACM-SIAM symposium on Discrete algorithms
Mechanism Design via Machine Learning
FOCS '05 Proceedings of the 46th Annual IEEE Symposium on Foundations of Computer Science
Mechanism design for single-value domains
AAAI'05 Proceedings of the 20th national conference on Artificial intelligence - Volume 1
On the competitive ratio of the random sampling auction
WINE'05 Proceedings of the First international conference on Internet and Network Economics
Online budgeted matching in random input models with applications to Adwords
Proceedings of the nineteenth annual ACM-SIAM symposium on Discrete algorithms
The hiring problem and Lake Wobegon strategies
Proceedings of the nineteenth annual ACM-SIAM symposium on Discrete algorithms
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
An online mechanism for ad slot reservations with cancellations
SODA '09 Proceedings of the twentieth Annual ACM-SIAM Symposium on Discrete Algorithms
Selling ad campaigns: online algorithms with cancellations
Proceedings of the 10th ACM conference on Electronic commerce
The adwords problem: online keyword matching with budgeted bidders under random permutations
Proceedings of the 10th ACM conference on Electronic commerce
Proceedings of the 10th ACM conference on Electronic commerce
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
Multi-parameter mechanism design and sequential posted pricing
Proceedings of the forty-second ACM symposium on Theory of computing
Online network design with outliers
ICALP'10 Proceedings of the 37th international colloquium conference on Automata, languages and programming
Algorithms and theory of computation handbook
Analysis of an automated auction with concurrent multiple unit acceptance capacity
ASMTA'10 Proceedings of the 17th international conference on Analytical and stochastic modeling techniques and applications
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
Incentives in online auctions via linear programming
WINE'10 Proceedings of the 6th international conference on Internet and network economics
Constrained non-monotone submodular maximization: offline and secretary algorithms
WINE'10 Proceedings of the 6th international conference on Internet and network economics
Online ranking for tournament graphs
WAOA'10 Proceedings of the 8th international conference on Approximation and online algorithms
The Hiring Problem and Lake Wobegon Strategies
SIAM Journal on Computing
Secretary problems and incentives via linear programming
ACM SIGecom Exchanges
Hiring a secretary from a poset
Proceedings of the 12th ACM conference on Electronic commerce
Buyback problem: approximate matroid intersection with cancellation costs
ICALP'11 Proceedings of the 38th international colloquim conference on Automata, languages and programming - Volume Part I
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
Online vertex-weighted bipartite matching and single-bid budgeted allocations
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
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
Budget feasible mechanism design: from prior-free to bayesian
STOC '12 Proceedings of the forty-fourth annual ACM symposium on Theory of 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
Approximation algorithms for online weighted rank function maximization under matroid constraints
ICALP'12 Proceedings of the 39th international colloquium conference on Automata, Languages, and Programming - Volume Part I
Online mechanism design (randomized rounding on the fly)
ICALP'12 Proceedings of the 39th international colloquium conference on Automata, Languages, and Programming - Volume Part II
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
Fast greedy algorithms in mapreduce and streaming
Proceedings of the twenty-fifth annual ACM symposium on Parallelism in algorithms and architectures
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
Submodular secretary problem and extensions
ACM Transactions on Algorithms (TALG)
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We study a generalization of the classical secretary problem which we call the "matroid secretary problem". In this problem, the elements of a matroid are presented to an online algorithm in random order. When an element arrives, the algorithm observes its value and must make an irrevocable decision regarding whether or not to accept it. The accepted elements must form an independent set, and the objective is to maximize the combined value of these elements. This paper presents an O(log k)-competitive algorithm for general matroids (where k is the rank of the matroid), and constant-competitive algorithms for several special cases including graphic matroids, truncated partition matroids, and bounded degree transversal matroids. We leave as an open question the existence of constant-competitive algorithms for general matroids. Our results have applications in welfare-maximizing online mechanism design for domains in which the sets of simultaneously satisfiable agents form a matroid.