A new proof for the first-fit decreasing bin-packing algorithm

This paper provides a new proof of a classical result of bin-packing, namely the $\text{11}\text{9}$ performance bound for the first-fit decreasing algorithm. In bin-packing, a list of real numbers in (0,1] is to be packed into a minimal number of bins, each of which holds a total of at most 1. The first-fit decreasing (FFD) algorithm packs each number in order of nonincreasing size into the first bin in which it fits. In his doctoral dissertation, D. S. Johnson (“Near-Optimal Bin Packing Algorithms,” Doctoral thesis, MIT, Cambridge, Mass., 1973) proved that for every list L, $\text{FFD}\text{(L) ?}\text{11}\text{9}\text{OPT}\text{(L) + 4}$, where FFD(L) and OPT(L) denote the number of bins used by FFD and an optimal packing, respectively. Unfortunately, his proof required more than 100 pages! This paper contains a much shorter and simpler proof that $\text{FFD}\text{(L) ?}\text{11}\text{9}\text{OPT}\text{(L) + 3}$.