Beating 1-1/e for ordered prophets

Melika Abolhassani, Soheil Ehsani, Hossein Esfandiari, MohammadTaghi HajiAghayi, Robert Kleinberg, Brendan Lucier
2017 Proceedings of the 49th Annual ACM SIGACT Symposium on Theory of Computing - STOC 2017  
Hill and Kertz studied the prophet inequality on iid distributions [The Annals of Probability 1982]. They proved a theoretical bound of 1-1/e on the approximation factor of their algorithm. They conjectured that the best approximation factor for arbitrarily large n is 1/1+1/e≈ 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
more » ... 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-iid distributions and discuss its applications in mechanism design.
doi:10.1145/3055399.3055479 dblp:conf/stoc/AbolhassaniEEHK17 fatcat:duznom5ivvad3mly2go6pdcrsi