Part of Advances in Neural Information Processing Systems 30 (NIPS 2017)
Moein Falahatgar, Yi Hao, Alon Orlitsky, Venkatadheeraj Pichapati, Vaishakh Ravindrakumar
PAC maximum selection (maxing) and ranking of $n$ elements via random pairwise comparisons have diverse applications and have been studied under many models and assumptions. With just one simple natural assumption: strong stochastic transitivity, we show that maxing can be performed with linearly many comparisons yet ranking requires quadratically many. With no assumptions at all, we show that for the Borda-score metric, maximum selection can be performed with linearly many comparisons and ranking can be performed with $\mathcal{O}(n\log n)$ comparisons.