LYCOS RETRIEVER 
Knapsack Problem
built 642 days ago
This book provides a full-scale presentation of all methods and techniques available for the solution of the Knapsack problem. This most basic combinatorial optimization problem appears explicitly or as a subproblem in a wide range of optimization models with backgrounds such diverse as cutting and packing, finance, logistics or general integer programming. This monograph spans the range from a comprehensive introduction of classical algorithmic methods to the unified presentation of the most recent and advanced results in this area many of them originating from the authors. The chapters dealing with particular versions and extensions of the Knapsack problem are self-contained to a high degree and provide a valuable source of reference for researchers. Due to its simple structure, the Knapsack problem is an ideal model for introducing solution techniques to students of computer science, mathematics and economics. The first three chapters give an in-depth treatment of several basic techniques, making the book ... suitable as underlying literature for courses in combinatorial optimization and approximation.
Source:
This paper focuses on a dynamic, continuous-time control generalization of the unbounded knapsack problem. This generalization implies that putting items in a knapsack takes time and has a due date. Specifically, the problem is characterized by a limited production horizon and a number of item types. Given an unbounded number of copies of each type of item, the items can be put into a knapsack at a controllable production rate subject to the available capacity. The demand for items is not known until the end of the production horizon. The objective is to collect items of each type in order to minimize shortage and surplus costs with respect to the demand.
Source:
The pseudo code for finding a solution to the 0-1 knapsack problem from the dynamic programming matrix follows; the algorithm will begin at knap[k][y] where k = a.length and y = b-1. The algorithm then finds the first occurrence the uppermost entry in column b with the value knap[k][y] - if this occurs in the row j then item j is an item selected for the optimal solution to the problem. In order to set up for finding the next item, mover over a[j] collumns and up one row and then repeat the process.
Source:
George Dantzig (1957) proposed a greedy approximation algorithm to solve the knapsack problem. His version sorts the essentials in decreasing order and then proceeds to insert them into the sack, starting from the first element (the greatest) until there is no longer space in the sack for more. If k is the maximum value of items that fit into the sack, the greedy algorithm is guaranteed to achieve at least a value of k/2.
Source:
When the Knapsack Algorithm is used in public key cryptography, the idea is to create two different knapsack problems. One is easy to solve, the other not. Using the easy knapsack, the hard knapsack is derived from it. The hard knapsack becomes the public key. The easy knapsack is the private key. The public key can be used to encrypt messages, but cannot be used to decrypt messages. The private key decrypts the messages.
Source:
An enumerative scheme is presented for the (0,1) knapsack problem as a specialization of the state enumeration method. Techniques are explored for rendering search procedures more efficient by systematic use of information generated during execution of the algorithm. The inequalities of Benders and Gomory-Johnson are exploited to yield implicit enumeration tests in the special case of the knapsack problem. In a comparative study of eight algorithms and of the utility of certain approximations and inequalities, computational results are given for twelve knapsack problems, each having ten (0,1) variables. The effectiveness of these enumerative algorithms are ... tested in a relatively simple framework.
Source:
MORE ABOUT
Knapsack Problem