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By G. Ausiello, M. Lucertini, P. Serafini (eds.)

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Notice that RA need not equal R;. Although R;FD .. 11/9, it is easy to give lists L for which OPT(L) - 2 and FFD(L) - 3, so that RFFD ~ 3/2. The asymptotic ratios seem to be a more reasonable measure of performance for the basic bin packing problem, but absolute ratios do come up in some of the work on related problems that we shall be discussing later. G. R. S. Johnson those just described. The quantity R;(t}, 0

Unfortunatly, although the model can be as accurate and comprehensive as desired, solution techniques are very complex and wotk effectively only for toy examples. Another measure of optimality is performance. Common performance objectives are minimum response time and maximum system throughput, but many others objectives can be considered as fault tolerance V1a alternative routing capabilities and minimum communication flow on the interconnection links or busses. In this framework distributed systems are commonly represented as queueing networks.

In [109] a slight improvement to FFD was also found. However, more significant improvements with an 0 (n log n) running time not much worse than that of FFD were discovered by Friesen and Langston [45] and by Garey and Johnson [54]. The first of these employs a hybrid algorithm: Both FFD and an algorithm called BEST TWO FIT are run on the input; the output is taken as the better of the two packings produced. 2, thus guaranteeing a weak upper bound on the minimum. 18333 ... , was proved.

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