An On-Line Scheduling Heuristic With Better Worst Case Ratio Than Graham's List Scheduling

case performance bounds for simple one-dimensional packing algorithms. SIAM J. A better algorithm for an ancient scheduling problem. Analysis of several task-scheduling algorithms for a model of multiprogramming computer systems. A new algorithm for on-line bin-packing. 44 43] G. Galambos and J. B. G. Frenk. A simple proof of Liang's lower bound for on-line bin packing and the extension to the parametric case. The parametric behaviour of the rst t decreasing bin-packing algorithm. 37] D. C. Fisher. Next-t packs a list and its reverse into the same number of bins. Oper. 42 12] J. Blazewicz and K. Ecker. A linear time algorithm for restricted bin packing and scheduling problems. Oper. Res. Lett., 2:80{83, 1983. 13] D. J. Brown. A lower bound for on-line one-dimensional bin-packing algorithms. analysis of an eecient algorithm for processor and storage allocation. 41 component sets (items) in the magazine can be in production. The problem is to plan the overall production process so as to minimize the number of setups. S. Khanna 77] mentions, in connection with studies of multimedia communications, that graph packing is an interesting special case. Items are edges (pairs of vertices) in a given graph G. An edge is packed in a bin if both of the vertices to which it is incident are in the bin, and so the problem is to pack the edges of G into as few bins as possible subject to the constraint that there can be at most C vertices in any bin. The approximability of this problem has yet to be studied. a dual version of the one-dimensional bin packing problem. J. Algorithms, 5:502{525, 1984. 6] B. S. Baker. A new proof for the rst-t decreasing bin-packing algorithm. A 5/4 algorithm for two-dimensional packing. A tight asymptotic bound for next-t-decreasing bin-packing. A better lower bound for on-line scheduling. 40 item is called available if all its immediate predecessors have already been packed. At each stage, the set of currently available items is sorted according to nonincreasing size, and each item is packed into the lowest indexed bin where it ts and no precedence constraint is violated. Note that, if no partial order is given, this algorithm produces the same packing as FFD. In general, however, its worst-case behavior is considerably worse. The APR is R 1 OFFD = 2; except in the strict model, where R 1 OFFD = 27 10. In this generalization, a …