Abstract
AbstractA recent paper by Schulze et al. (Math Methods Oper Res 92(1):107–132, 2020) presented the Rectangular Knapsack Problem (Rkp) as a crucial subproblem in the study on the Cardinality-constrained Bi-objective Knapsack Problem (Cbkp). To this end, they started an investigation into its complexity and approximability. The key results are an -hardness proof for a more general scenario than Rkp, and a 4.5-approximation for Rkp, raising the question of improvements for either result. In this note we settle both questions conclusively: we show that (a) Rkp is indeed -hard in the considered setting (and even in more restricted settings), and (b) there exists both a pseudopolynomial algorithm and a fully-polynomial time approximation scheme (i.e., efficient approximability within any desired ratio $$\alpha >1$$
α
>
1
) for Rkp.
Publisher
Springer Science and Business Media LLC
Subject
Management Science and Operations Research,General Mathematics,Software
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