An optimal algorithm for on-line bipartite matching
STOC '90 Proceedings of the twenty-second annual ACM symposium on Theory of computing
SODA '04 Proceedings of the fifteenth annual ACM-SIAM symposium on Discrete algorithms
Approximating Matches Made in Heaven
ICALP '09 Proceedings of the 36th International Colloquium on Automata, Languages and Programming: Part I
Online Stochastic Matching: Beating 1-1/e
FOCS '09 Proceedings of the 2009 50th Annual IEEE Symposium on Foundations of Computer Science
Online bipartite matching with unknown distributions
Proceedings of the forty-third annual ACM symposium on Theory of computing
Online bipartite matching with random arrivals: an approach based on strongly factor-revealing LPs
Proceedings of the forty-third annual ACM symposium on Theory of computing
One to rule them all: a general randomized algorithm for buffer management with bounded delay
ESA'11 Proceedings of the 19th European conference on Algorithms
Online vertex-weighted bipartite matching and single-bid budgeted allocations
Proceedings of the twenty-second annual ACM-SIAM symposium on Discrete Algorithms
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Consider the following problem of serving impatient users: we are given a set of customers we would like to serve. We can serve at most one customer in each time step (getting value vi for serving customer i). At the end of each time step, each as-yet-unserved customer i leaves the system independently with probability qi, never to return. What strategy should we use to serve customers to maximize the expected value collected? The standard model of competitive analysis can be applied to this problem: picking the customer with maximum value gives us half the value obtained by the optimal algorithm, and using a vertex weighted online matching algorithm gives us 1-1/e ~ 0.632 fraction of the optimum. As is usual in competitive analysis, these approximations compare to the best value achievable by an clairvoyant adversary that knows all the coin tosses of the customers. Can we do better? We show an upper bound of ~0.648 if we compare our performance to such an clairvoyant algorithm, suggesting we cannot improve our performance substantially. However, these are pessimistic comparisons to a much stronger adversary: what if we compare ourselves to the optimal strategy for this problem, which does not have an unfair advantage? In this case, we can do much better: in particular, we give an algorithm whose expected value is at least 0.7 of that achievable by the optimal algorithm. This improvement is achieved via a novel rounding algorithm, and a non-local analysis.