A Polynomial Time Approximation Scheme for the Multiple Knapsack Problem
نویسندگان
چکیده
منابع مشابه
A Polynomial Time Approximation Scheme for the Multiple Knapsack Problem
The multiple knapsack problem (MKP) is a natural and well-known generalization of the single knapsack problem and is defined as follows. 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). The goal is to find a subset of items of maximum profit such that they have a feasible packing in the bins. MKP is...
متن کاملA 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.
متن کاملImproved Fully Polynomial time Approximation Scheme for the 0-1 Multiple-choice Knapsack Problem
In this paper the 0-1 Multiple-Choice Knapsack Problem (0-1 MCKP), a generalization of the classical 0-1 Knapsack problem, is addressed. We present a fast Fully Polynomial Time Approximation Scheme (FPTAS) for the 0-1 MCKP, which yields a better time bound than known algorithms. In particular it produces a (1+ ) approximate solution and runs in O(nm/ ) time, where n is the number of items and m...
متن کاملCsc5160: Combinatorial Optimization and Approximation Algorithms Topic: Polynomial Time Approximation Scheme 17.1 Polynomial Time Approximation Scheme 17.2 Knapsack Problem
In previous chapters we have seen the definition of a constant factor approximation algorithm. In this chapter, we will introduce the notion of a polynomial time approximation scheme (PTAS), which allows approximability to any required degree. To illustrate how PTAS works, we will study two examples, including the knapsack problem and the bin packing problem. The dynamic programming technique w...
متن کاملA Deterministic Polynomial-Time Approximation Scheme for Counting Knapsack Solutions
Given n elements with nonnegative integer weights w1, . . . , wn and an integer capacity C, we consider the counting version of the classic knapsack problem: find the number of distinct subsets whose weights add up to at most the given capacity. We give a deterministic algorithm that estimates the number of solutions to within relative error 1±ε in time polynomial in n and 1/ε (fully polynomial...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: SIAM Journal on Computing
سال: 2005
ISSN: 0097-5397,1095-7111
DOI: 10.1137/s0097539700382820