Ranking and selection (R&S), which aims to select the best alternative with
the largest mean performance from a finite set of alternatives, is a classic
research topic in simulation optimization. Recently, considerable attention has
turned towards the large-scale variant of the R&S problem which involves a
large number of alternatives. Ideal large-scale R&S procedures should be sample
optimal, i.e., the total sample size required to deliver an asymptotically
non-zero probability of correct selection (PCS) grows at the minimal order
(linear order) in the number of alternatives, but not many procedures in the
literature are sample optimal. Surprisingly, we discover that the na\"ive
greedy procedure, which keeps sampling the alternative with the largest running
average, performs strikingly well and appears sample optimal. To understand
this discovery, we develop a new boundary-crossing perspective and prove that
the greedy procedure is indeed sample optimal. We further show that the derived
PCS lower bound is asymptotically tight for the slippage configuration of means
with a common variance. Moreover, we propose the explore-first greedy (EFG)
procedure and its enhanced version (EFG+ procedure) by adding an exploration
phase to the na\"ive greedy procedure. Both procedures are proven to be sample
optimal and consistent. Last, we conduct extensive numerical experiments to
empirically understand the performance of our greedy procedures in solving
large-scale R&S problems