An FPTAS for the parametric knapsack problem

An FPTAS for the parametric knapsack problem

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...

An 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. ...

An FPTAS for Knapsack , and K - Center

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(...

A Faster FPTAS for #Knapsack

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...