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
Greedy in approximation algorithms
ESA'06 Proceedings of the 14th conference on Annual European Symposium - Volume 14
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
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
Online Ad Assignment with Free Disposal
WINE '09 Proceedings of the 5th International Workshop on Internet and Network Economics
Online stochastic packing applied to display ad allocation
ESA'10 Proceedings of the 18th annual European conference on Algorithms: Part I
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
Online bipartite matching with unknown distributions
Proceedings of the forty-third annual ACM symposium on Theory of computing
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
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
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
Recent advances on the matroid secretary problem
ACM SIGACT News
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We examine online matching problems with applications to Internet advertising reservation systems. Consider an edge-weighted bipartite graph G (L *** R , E ). We develop an 8-competitive algorithm for the following secretary problem: Initially given R , and the size of L , the algorithm receives the vertices of L sequentially, in a random order. When a vertex l *** L is seen, all edges incident to l are revealed, together with their weights. The algorithm must immediately either match l to an available vertex of R , or decide that l will remain unmatched. In [5], the authors show a 16-competitive algorithm for the transversal matroid secretary problem, which is the special case with weights on vertices, not edges. (Equivalently, one may assume that for each l *** L , the weights on all edges incident to l are identical.) We use a very similar algorithm, but simplify and improve the analysis to obtain a better competitive ratio for the more general problem. Our analysis is easily extended to obtain competitive algorithms for a class of similar problems, such as to find disjoint sets of edges in hypergraphs where edges arrive online. We also introduce secretary problems with adversarially chosen groups . Finally, we give a 2e -competitive algorithm for the secretary problem on graphic matroids, where, with edges appearing online, the goal is to find a maximum-weight acyclic subgraph of a given graph.