Tight Worst-Case Performance Bounds for Next-k-Fit Bin Packing

Abstract. The bin packing problem is to pack a list of reals in (0, 1] into unit-capacity bins using the minimum number of bins. Let R[A] be the limiting worst value for the ratio A(L)/L* as L* goes to x, where A(L) denotes the number ofbins used in the approximation algorithm A, and L* denotes the minimum number ofbins needed to pack L. Obviously, R[A] reflects the worst-case behavior of A. For Next-k-Fit(NkF for short, k _> 2), which is a linear time approximation algorithm for bin packing, it was known that 1.7 -k 3 lo(k-1) -< R[NkF] _< 2. In this paper, a tight bound R[NkF] 1.7 + o(-1) is proved.