Competitive analysis of incentive compatible on-line auctions
Proceedings of the 2nd ACM conference on Electronic commerce
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
Online ascending auctions for gradually expiring items
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
Selling ad campaigns: online algorithms with cancellations
Proceedings of the 10th ACM conference on Electronic commerce
Optimal Algorithms for the Online Time Series Search Problem
COCOA '09 Proceedings of the 3rd International Conference on Combinatorial Optimization and Applications
Algorithms for Secretary Problems on Graphs and Hypergraphs
ICALP '09 Proceedings of the 36th Internatilonal Collogquium on Automata, Languages and Programming: Part II
Multi-parameter mechanism design and sequential posted pricing
Proceedings of the forty-second ACM symposium on Theory of computing
Optimal algorithms for the online time series search problem
Theoretical Computer Science
Constrained non-monotone submodular maximization: offline and secretary algorithms
WINE'10 Proceedings of the 6th international conference on Internet and network economics
Secretary problems and incentives via linear programming
ACM SIGecom Exchanges
Delay-tolerant delivery of quality information in ad hoc networks
Journal of Parallel and Distributed Computing
Hiring a secretary from a poset
Proceedings of the 12th ACM conference on Electronic commerce
Online algorithms for the multiple time series search problem
Computers and Operations Research
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
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
Budget feasible mechanism design: from prior-free to bayesian
STOC '12 Proceedings of the forty-fourth annual ACM symposium on Theory of computing
Interviewing secretaries in parallel
Proceedings of the 13th ACM Conference on Electronic Commerce
Optimal, quality-aware scheduling of data consumption in mobile ad hoc networks
Journal of Parallel and Distributed Computing
Secretary problems with convex costs
ICALP'12 Proceedings of the 39th international colloquium conference on Automata, Languages, and Programming - Volume Part I
Geometry of online packing linear programs
ICALP'12 Proceedings of the 39th international colloquium conference on Automata, Languages, and Programming - Volume Part I
On the use of optimal stopping theory for improving cache consistency
WISE'12 Proceedings of the 13th international conference on Web Information Systems Engineering
Multivariate context collection in mobile sensor networks
Computer Networks: The International Journal of Computer and Telecommunications Networking
Truthful incentives in crowdsourcing tasks using regret minimization mechanisms
Proceedings of the 22nd international conference on World Wide Web
Recent advances on the matroid secretary problem
ACM SIGACT News
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The classical secretary problem studies the problem of selecting online an element (a "secretary") with maximum value in a randomly ordered sequence. The difficulty lies in the fact that an element must be either selected or discarded upon its arrival, and this decision is irrevocable. Constant-competitive algorithms are known for the classical secretary problems (see, e.g., the survey of Freeman [7]) and several variants. We study the following two extensions of the secretary problem: • In the discounted secretary problem, there is a time-dependent "discount" factor d(t), and the benefit derived from selecting an element/secretary e at time t is d(t) · v(e). For this problem with arbitrary (not necessarily decreasing) functions d(t), we show a constant-competitive algorithm when the expected optimum is known in advance. With no prior knowledge, we exhibit a lower bound of Ω(log n/log log n), and give a nearly-matching O(log n)-competitive algorithm. • In the weighted secretary problem, up to K secretaries can be selected; when a secretary is selected (s)he must be irrevocably assigned to one of K positions, with position k having weight w(k), and assigning object/secretary e to position k has benefit w(k) · v(e). The goal is to select secretaries and assign them to positions to maximize Σe, k w(k) · v(e) · xek where xek is an indicator variable that secretary e is assigned position k. We give constant-competitive algorithms for this problem. Most of these results can also be extended to the matroid secretary case (Babaioff et al. [2]) for a large family of matroids with a constant-factor loss, and an O(log rank) loss for general matroids. These results are based on a reduction from various matroids to partition matroids which present a unified approach to many of the upper bounds of Babaioff et al. These problems have connections to online mechanism design (see, e.g., Hajiaghayi et al. [9]). All our algorithms are monotone, and hence lead to truthful mechanisms for the corresponding online auction problems.