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In a seminal paper, Karp, Vazirani, and Vazirani show that a simple ranking algorithm achieves a competitive ratio of 1-1/e for the online bipartite matching problem in the standard adversarial model, where the ratio of 1-1/e is also shown to be optimal. Their result also implies that in the random arrivals model defined by Goel and Mehta, where the online nodes arrive in a random order, a simple greedy algorithm achieves a competitive ratio of 1-1/e. In this paper, we study the ranking algorithm in the random arrivals model, and show that it has a competitive ratio of at least 0.696, beating the 1-1/e ≈ 0.632 barrier in the adversarial model. Our result also extends to the i.i.d. distribution model of Feldman et al., removing the assumption that the distribution is known.
Mahdian et al. (Mon,) studied this question.
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