A fully polynomial time approximation scheme for the Replenishment Storage problem

A New Fully Polynomial Approximation Scheme for the Knapsack Problem

A new fully polynomial approximation scheme (FPTAS) is presented for the classical 0{1 knapsack problem. It considerably improves the space requirements. The two best previously known approaches need O(n+1=" 3) and O(n1=") space, respectively. Our new approximation scheme requires only O(n + 1=" 2) space while also reducing the running time.

An Efficient Polynomial-Time Approximation Scheme for the Joint Replenishment Problem

We give an efficient polynomial-time approximation scheme (EPTAS) for the Joint Replenishment Problem (JRP) with stationary demand. Moreover, using a similar technique, we give a PTAS for the capacitated JRP with non-stationary demand but constant size capaci-

A Fully Polynomial Time Approximation Scheme for Packing While Traveling

Understanding the interactions between different combinatorial optimisation problems in real-world applications is a challenging task. Recently, the traveling thief problem (TTP), as a combination of the classical traveling salesperson problem and the knapsack problem, has been introduced to study these interactions in a systematic way. We investigate the underlying non-linear packing while tra...

A new fully polynomial time approximation scheme for the interval subset sum problem

The interval subset sum problem (ISSP) is a generalization of the wellknown subset sum problem. Given a set of intervals {[ai,1, ai,2]} n i=1 and a target integer T, the ISSP is to find a set of integers, at most one from each interval, such that their sum best approximates the target T but cannot exceed it. In this paper, we first study the computational complexity of the ISSP. We show that th...

A New Fully Polynomial Time Approximation Scheme for the Knapsack Problem