Apart from its inherent theoretical interest as a common generalization of the well-studied knapsack and bin packing problems, it appears to be the strongest special case of GAP that is not APX-hard.
The main result of this paper is a polynomial time approximation scheme for MKP. GAP is APX-hard and a 2-approximation for it is implicit in the work of Shmoys and Tardos, and thus far, this was also the best known approximation for MKP. MKP is a special case of the Generalized Assignment problem (GAP) where the profit and the size of an item can vary based on the specific bin that it is assigned to.
The goal is to find a subset of items of maximum profit such that they have a feasible packing in the bins.
We are given a set of n items and m bins (knapsacks) such that each item i has a profit p(i) and a size s(i), and each bin j has a capacity c(j). N2 - The Multiple Knapsack problem (MKP) is a natural and well known generalization of the single knapsack problem and is defined as follows. T1 - PTAS for the Multiple Knapsack problem An interesting and novel aspect of our approach is an approximation preserving reduction from an arbitrary instance of MKP to an instance with O(log n) distinct sizes and profits.", Thus our results help demarcate the boundary at which instances of GAP become APX-hard. We substantiate this by showing that slight generalizations of MKP are APX-hard. An interesting and novel aspect of our approach is an approximation preserving reduction from an arbitrary instance of MKP to an instance with O(log n) distinct sizes and profits.Ībstract = "The Multiple Knapsack problem (MKP) is a natural and well known generalization of the single knapsack problem and is defined as follows. The Multiple Knapsack problem (MKP) is a natural and well known generalization of the single knapsack problem and is defined as follows.
0 kommentar(er)
