Competitive analysis of the top-K ranking problem
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Motivated by applications in recommender systems, web search, social choice and crowdsourcing, we consider the problem of identifying the set of top K items from noisy pairwise comparisons. In our setting, we are non-actively given r pairwise comparisons between each pair of n items, where each comparison has noise constrained by a very general noise model called the strong stochastic transitivity (SST) model. We analyze the competitive ratio of algorithms for the top-K problem. In particular, we present a linear time algorithm for the top-K problem which has a competitive ratio of Õ(√(n)); i.e. to solve any instance of top-K, our algorithm needs at most Õ(√(n)) times as many samples needed as the best possible algorithm for that instance (in contrast, all previous known algorithms for the top-K problem have competitive ratios of Ω̃(n) or worse). We further show that this is tight: any algorithm for the top-K problem has competitive ratio at least Ω̃(√(n)).
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