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

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Man. , 1977. [21] DE JULIO, LUCERTINI, SACCA': Un algoritmo efficiente per la decompo sizione ottima di macchine sequenziali. Conf. AIRO, 1978. [22] DENNING: Vurtua1 memory. Compo Survey, 1970. [23] DENNING, BUZEN: The operational analysis of queueing network models. Compo Surveys, 1978. [24] DONATH, HOFFMAN: Lower bounds for the partitioning of Graphs. IBM J. of Res. , 1973. [25] DOWDY, FOSTER: Comparative models of the file assignment problem. ACM Compo Surveys, 1982. [26] DUTTA, KOEHLER, WHINSTON: On optimal allocation in a distributed processing environment.

FIRST FIT seems to perform poorly when the large items occur at the end of the list. DECREASING seeks to avoid this effect by first The algorithm FIRST FIT ordering the items so that s (Pt) ~ s (P2) ~ '" ~ S (PrJ), and then applying FIRST FIT to the reordered list. For this algorithm it can be shown (with considerable difficulty [4,69,72]) that for all lists L, 11 FFD(L) :E;; 9'OPT(L)+4 and, once more, this is the best ratio possible, as illustrated in Figure 3. 55 Approximation Algorithms for Bin-Packing - An Updated Survey /11/ IIIII 4" -2E 1 4"-2E 1 1 4" -2E 1 4"+E 4"-2E 1 4"+2E 1 4"+E 4" -2E 1 4"+2E 1 4"+E 4" -2c 1 4"+E 1 1 4" -2E 1 1 2+E 6N bins 6N bins 3N bins OPT(L)=9N Figure 3.

The basic concepts of approximate solution of optimization problems are also presented in the same volume and in 30 G. Sahni: Fundamentals of computer algorithms 3 computer Science Press, 1978. H. Steiglitz: Combinatorial optimiza- tion: Algorithms and complexitY3 Prentice Hall, 1982. The following papers provide a more precise approach to the characterization of classes of NP-complete optimization problems: - Paz ,A. Moran: NP-optimization problems and their approximation, Proc 4th Int. Symposium on Automatic 3 Languages and Programming 3 LNCS, Springer Verlag, 1977.