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An FPTAS for the Δ-modular multidimensional knapsack problem [article]

D. V. Gribanov
2021 arXiv   pre-print
In this note, we show that the m-dimensional knapsack problem with a Δ-modular constraints matrix admits an FPTAS, whose complexity bound depends on Δ linearly.  ...  But, an FPTAS still can exist for some other particular cases of the problem.  ...  Additionally, Corollary 2 gives currently best bound O(n·∆ 2 1 ) for the classical 1-dimensional bounded knapsack problem, see Remark 2. The analogue result can be stated for our FPTAS.  ... 
arXiv:2103.07257v4 fatcat:ls3utbfo7jbetg2kpmuv3q4zha

Improvement/Extension of Modular Systems as Combinatorial Reengineering (Survey) [article]

Mark Sh. Levin
2013 arXiv   pre-print
The paper describes development (improvement/extension) approaches for composite (modular) systems (as combinatorial reengineering).  ...  The strategies are based on combinatorial optimization problems (e.g., multicriteria selection, knapsack problem, multiple choice problem, combinatorial synthesis based on morphological clique problem,  ...  The problem was firstly formulated for designing an overlay structure of a modular software system in [26] .  ... 
arXiv:1304.4965v1 fatcat:gxnwbp4tbrcu5opncbab372cha

Birand_columbia_0054D_12551.pdf [article]

The success of the Internet can be largely attributed to its modular architecture and its high level of abstraction.  ...  As a result, the Internet is an extremely heterogeneous network in which a multitude of wireless, electronic, and optical devices coexist.  ...  We now describe an algorithm for JTK based on the well-known Multidimensional Multiplechoice Knapsack (MMK) Problem [84] .  ... 
doi:10.7916/d82v2psm fatcat:blvxrsnpzbf7jekstnqzmxx52q