Abstract
In this paper, we analyze the average-case performance of the Modified Harmonic algorithm for bin packing. We first analyze the average-case performance for arbitrary distribution of item sizes over (0, 1]. This analysis is based on the following result. Let f 1 and f 2 be two linear combinations of random variables {n i} kn=1 , where the N is have a joint multinomial distribution for each \(n = \sum\limits_{i = 1}^k {N_i }\). Let E(f 1)≠0, and E(f 2)↮0. Then \(\mathop {\lim }\limits_{n \to \infty }\) E(max(f 1, f 2))/n=\(\mathop {\lim }\limits_{n \to \infty }\) max(E(f 1), E(f 2))/n. We then consider the special case when the item sizes are uniformly distributed over (0, 1], and obtain optimal values for the parameters of the algorithm. For these values of the parameters, the average-case performance ratio is less than 1.19. This compares well with the performance ratio 1.2865... of the Harmonic algorithm.
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© 1986 Springer-Verlag Berlin Heidelberg
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Ramanan, P., Tsuga, K. (1986). Average-case analysis of the Modified Harmonic algorithm. In: Nori, K.V. (eds) Foundations of Software Technology and Theoretical Computer Science. FSTTCS 1986. Lecture Notes in Computer Science, vol 241. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-17179-7_11
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DOI: https://doi.org/10.1007/3-540-17179-7_11
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