Approximating the product knapsack problem

نویسندگان

چکیده

Abstract We consider the product knapsack problem, which is variant of classical 0-1 problem where objective consists maximizing profits selected items. These are allowed to be positive or negative. present first fully polynomial-time approximation scheme for known weakly -hard. Moreover, we analyze quality achieved by a natural extension greedy procedure problem.

برای دانلود باید عضویت طلایی داشته باشید

برای دانلود متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید

اگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید

منابع مشابه

Approximating the Incremental Knapsack Problem

We consider the 0–1 Incremental Knapsack Problem (IKP) where the capacity grows over time periods and if an item is placed in the knapsack in a certain period, it cannot be removed afterwards. The contribution of a packed item in each time period depends on its profit as well as on a time factor which reflects the importance of the period in the objective function. The problem calls for maximiz...

متن کامل

Approximating the Orthogonal Knapsack Problem for Hypercubes

Given a list of d-dimensional cuboid items with associated profits, the orthogonal knapsack problem asks for a packing of a selection with maximal profit into the unit cube. We restrict the items to hypercube shapes and derive a ( 5 4 + )-approximation for the twodimensional case. In a second step we generalize our result to a ( 2 +1 2d + )approximation for d-dimensional packing.

متن کامل

Approximating the solution of a dynamic , stochastic multiple knapsack problem

We model an environment where orders arrive probabilistically over time, with their revenues and capacity requirements becoming known upon arrival. The decision is whether to accept an order, receiving a reward and reserving capacity, or reject an order, freeing capacity for possible future arrivals. We model the dynamic, stochastic multiple knapsack problem (DSMKP) with stochastic dynamic prog...

متن کامل

A Mildly Exponential Time Algorithm for Approximating the Number of Solutions to a Multidimensional Knapsack Problem

We describe a 2O(r √ n(logn)5/2) ǫ −2 time randomized algorithm which estimates the number of feasible solutions of a multidimensional knapsack problem within 1± ǫ of the exact number. (Here r is the number of constraints and n is the number of integer variables.) The algorithm

متن کامل

The Knapsack Problem

Suppose we are planning a hiking trip; and we are, therefore, interested in filling a knapsack with items that are considered necessary for the trip. There are N different item types that are deemed desirable; these could include bottle of water, apple, orange, sandwich, and so forth. Each item type has a given set of two attributes, namely a weight (or volume) and a value that quantifies the l...

متن کامل

ذخیره 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: Optimization Letters

سال: 2021

ISSN: ['1862-4480', '1862-4472']

DOI: https://doi.org/10.1007/s11590-021-01760-x