Beating 1-1/e for ordered prophets - Abolhassani, Melika; Ehsani, Soheil; Esfandiari, Hossein; Hajiaghayi, MohammadTaghi; Kleinberg, Robert; Lucier, Brendan (STOC 2017, 2017)
Hill and Kertz studied the prophet inequality on iid distributions [The Annals of Probability 1982]. They proved a theoretical bound of 1 â 1/e on the approximation factor of their algorithm. They conjectured that the best approximation factor for arbitrarily large n is 1/1+1/eâ 0.731. This conjecture remained open prior to this paper for over 30 years. In this paper we present a threshold-based algorithm for the prophet inequality with n iid distributions. Using a nontrivial and novel approach we show that our algorithm is a 0.738-approximation algorithm. By beating the bound of 1/1+1/e, this refutes the conjecture of Hill and Kertz. Moreover, we generalize our results to non-uniform distributions and discuss its applications in mechanism design.