Average Case Analysis of Bounded Space Bin Packing Algorithms

Abstract We consider the one-dimensional bin packing problem and analyze the average case performance of bounded space algorithms. The analysis covers a wide variety of bin packing algorithms including Next-K Fit, K-Bounded Best Fit and Harmonic algorithms, as well as of others. We assume discrete item sizes, an assumption which is true in most real-world applications of bin packing. We present a Markov chains method which is general enough to calculate results for any i.i.d. discrete item size distribution. The paper presents many results heretofore unknown or conjectured from simulation. Some of the results are surprising as they differ considerably from results for continuous distributions.

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