Basic Analysis of Bin-Packing Heuristics

The benchmarks have been performed using an Intel Celeron M 1.5 GHz. The results are not too surprising: Obviously, the Next-Fit heuristic is fastest because only 1 bin has to be managed. However, due to the efficient data structure (a priority queue) that has been used for the Max-Rest heuristic, this heuristic will generally be almost as fast as Next-Fit. Furthermore, the implementation of the Best-Fit heuristic has a worst-case running time of O(Kn), where K is the maximum weight. Thus, the slowest algorithms are First-Fit and First-Fit-Decreasing. Detailed results can be studied in the table below. In each set, the best solutions are marked using the dagger symbol “†”. The timing is not accurate for the small running times. This is due to the CLOCKS PER SEC macro that has been used for the benchmarks. Hence, in some cases, the same running times will appear. This means that the running times differ by a very small amount (measured in “raw” CPU cycles). A value of 0 signifies that the measurement is outside the notable range. The algorithms have been compiled with the -O3 optimizations of the g++ compiler. All heuristics have been abbreviated to fit in the table. Thus, MR is Max-Rest, for example. The +-signs after the algorithm names specify whether an optimized version of the algorithm has been used. For implementation details, refer to table 2 on page 6.