Competitive analysis of the top- K ranking problem
SODA '17: Symposium on Discrete Algorithms Barcelona Spain January, 2017(2017)
摘要
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 [EQUATION]; i.e. to solve any instance of top-K, our algorithm needs at most [EQUATION] 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 O(n) or worse). We further show that this is tight: any algorithm for the top-K problem has competitive ratio at least [EQUATION].
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