Bin-packing and matchings in threshold graphs Original Research Article

To each z ϵ (0, 1]n there is a corresponding bin-packing problem and a corresponding threshold graph G(z). Under the assumption that the components of z are independent and uniformly distributed on (0, 1]the graphs G(z) are also uniformly distributed. A bin-packing solution found by some well known version 2FFD of the heuristic First Fit Decreasing applied to z defines a maximum matching in G(z). This fact is used to derive an explicit expression for the excepted waste of 2FFD as a function of n. In the limit, the expected waste is found to be (√2π)−1√n.