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- W1542821710 abstract "We consider variants of the classic bin packing and multiple knapsack problems, in which sets of items of different classes (colors) need to be placed in bins; the items mayha ve different sizes and values. Each bin has a limited capacity, and a bound on the number of distinct classes of items it can hold. In the class-constrained multiple knapsack (CCMK) problem, our goal is to maximize the total value of packed items, whereas in the class-constrained bin-packing (CCBP), we seek to minimize the number of (identical) bins, needed for packing all the items. We give a polynomial time approximation scheme (PTAS) for CCMK and a dual PTAS for CCBP. We also show that the 0-1 class-constrained knapsack admits a fully polynomial time approximation scheme, even when the number of distinct colors of items depends on the input size. Finally, we introduce the generalized class-constrained packing problem (GCCP), where each item mayh ave more than one color. We show that GCCP is APX-hard, alreadyf or the case of a single knapsack, where all items have the same size and the same value.Our optimization problems have several important applications, including storage management for multimedia systems, production planning, and multiprocessor scheduling." @default.
- W1542821710 created "2016-06-24" @default.
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- W1542821710 date "2000-01-01" @default.
- W1542821710 modified "2023-10-14" @default.
- W1542821710 title "Polynomial Time Approximation Schemes for Class-Constrained Packing Problems" @default.
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- W1542821710 doi "https://doi.org/10.1007/3-540-44436-x_24" @default.
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