A faster FPTAS for the Unbounded Knapsack Problem
نویسندگان
چکیده
منابع مشابه
A Faster FPTAS for the Unbounded Knapsack Problem
The Unbounded Knapsack Problem (UKP) is a well-known variant of the famous 0-1 Knapsack Problem (0-1 KP). In contrast to 0-1 KP, an arbitrary number of copies of every item can be taken in UKP. Since UKP is NP-hard, fully polynomial time approximation schemes (FPTAS) are of great interest. Such algorithms find a solution arbitrarily close to the optimum OPT(I), i.e. of value at least (1− ε)OPT(...
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Given a set W = {w1, . . . , wn} of non-negative integer weights and an integer C, the #Knapsack problem asks to count the number of distinct subsets of W whose total weight is at most C. In the more general integer version of the problem, the subsets are multisets. That is, we are also given a set {u1, . . . , un} and we are allowed to take up to ui items of weight wi. We present a determinist...
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In this paper, we investigate the parametric knapsack problem, in which the item profits are affine functions depending on a real-valued parameter. The aim is to provide a solution for all values of the parameter. It is well-known that any exact algorithm for the problemmay need to output an exponential number of knapsack solutions. We present a fully polynomial-time approximation scheme (FPTAS...
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The Subset-Sums Ratio problem (SSR) is an optimization problem in which, given a set of integers, the goal is to find two subsets such that the ratio of their sums is as close to 1 as possible. In this paper we develop a new FPTAS for the SSR problem which builds on techniques proposed in [D. Nanongkai, Simple FPTAS for the subset-sums ratio problem, Inf. Proc. Lett. 113 (2013)]. One of the key...
متن کاملAn FPTAS for the Knapsack Problem with Parametric Weights
In this paper, we investigate the parametric weight knapsack problem, in which the item weights are affine functions of the formwi(λ) = ai + λ ·bi for i ∈ {1, . . . ,n} depending on a real-valued parameter λ. The aim is to provide a solution for all values of the parameter. It is well-known that any exact algorithm for the problem may need to output an exponential number of knapsack solutions. ...
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ژورنال
عنوان ژورنال: European Journal of Combinatorics
سال: 2018
ISSN: 0195-6698
DOI: 10.1016/j.ejc.2017.07.016