Optimal bin covering with items of random size
SIAM Journal on Computing
A note for optimal bin packing and optimal bin covering with items of random size
SIAM Journal on Computing
Probabilistic analysis of algorithms for dual bin packing problems
Journal of Algorithms
Analysis of Several Task-Scheduling Algorithms for a Model of Multiprogramming Computer Systems
Journal of the ACM (JACM)
Better approximation algorithms for bin covering
SODA '01 Proceedings of the twelfth annual ACM-SIAM symposium on Discrete algorithms
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In the bin covering problem we are asked to pack a list X(n) = (x"1, x"2, ... , x"n) of n items, each with size no larger than one, into the maximum number of bins such that the sum of the sizes of the items in each bin is at least one. In this article we analyze the asymptotic average-case behavior of the Iterated-Lowest-Fit-Decreasing (ILFD) algorithm proposed by Assmann et al. Let OPT(X(n)) denote the maximum number of bins that can be covered by X(n) and let ILFD(X(n)) denote the number of bins covered by the ILFD algorithm. Assuming that X(n) is a random sample from an arbitrary probability measure @m over [0, 1], we show the existence of a constant d(@m) and a constructible sequence {@X(n) @e [0,1]^n: n = 1} such that and |(ILFD(@X(n))n) - d(@m)|@? 1n and lim"n"-"~ (ILFD(X(n))n) = d(@m), almost surely. Since (ILFD(X(n))n) always lies in [0,1], it follows that lim"n"-"~ (E[ILFD(X(n))]n) = d(@m) as well. We also show that the expected values of the ratio r"I"L"F"D(X(n)) = OPT(X(n))ILFD(X(n)), over all possible probability measures for X(n), lie in [1, 43], the same range as the deterministic case.