“A posteriori” evaluation of bin packing approximation algorithms

z-Approximations

“…If α = 1 then we might get a solution that is as bad as the worst solution. Several other authors have independently recognized the advantages of the z-measure: Ausiello et al [4] denote it as "the proximity degree" of a solution and attribute its formulation to [1], where a constant factor zapproximation is given for max cut (see also Aiello et al [2]). Ausiello et al [5] show that max-subset sum obtains a fully polynomial z-approximation scheme, while max-clique and max cut do not.…”

On a posterior evaluation of a simple greedy method for set packing

“…However, it remains a challenge to determine the quality of a single computed solution via a heuristic without actually knowing the optimal solution. One of the first instances of a posterior analysis for hard discrete optimization problems was by Aiello et al [1] where a bin packing problem was analyzed where the size of the first item placed in the last bin employed in an approximate solution is used to classify whether the solution is optimal or better than known "a priori" bounds.…”