A faster FPTAS for knapsack problem with cardinality constraint

We study the K -item knapsack problem ( i.e. , 1.5-dimensional problem), a generalization of famous 0–1 1-dimensional problem) in which an upper bound is imposed on number items selected. This fundamental importance and known to have broad range applications various fields. It well that, there no fully polynomial time approximation scheme (FPTAS) for d -dimensional when ? 2 unless P = NP. While admit FPTAS, complexity all existing FPTASs has high dependency cardinality error ? could result inefficiencies especially ? 1 increase. The current best results are due Mastrolilli Hutter (2006), two schemes presented exhibiting space–time tradeoff-one with O n + z / ) space 3 another that requires run-time 4 but only needs space, where min { } . In this paper we close tradeoff exhibited (2006) by designing new FPTAS running ˜ while simultaneously reaching notation hides terms poly-logarithmic Our provides improvements state-of-the-art algorithms respectively, first achieves independent (up logarithmic factors) under fixed Another salient feature our algorithm it better bounds than very standard over parameter regimes