A provably fast linear-expected-time maxima-finding algorithm

In a recent paper Bentleyet al. [1] presented some fast (low-multiplicative constants) linear-expected-time algorithms for finding the maxima ofN points chosen independently identically distributed (i.i.d.) from a Component Independent (CI) distribution. They also presented another algorithm, the Move-To-Front (MTF) algorithm, which empirical evidence suggests runs faster than the other algorithms. They conjectured that the MTF algorithm runs inN+o(N) expected time. In this paper we prove their conjecture forN points chosen i.i.d. from any two-dimensional distribution. The proof mixes probabilistic and amortized techniques.