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The knapsack problem
"... Abstract Have you ever wondered about how heavy one can fill his knapsack? No? That does not matter. You will get the answer in this paper. There are several algorithms for the simple knapsack problem and the knapsack problem. Four of them will be shown and proved in this paper. ..."
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Abstract Have you ever wondered about how heavy one can fill his knapsack? No? That does not matter. You will get the answer in this paper. There are several algorithms for the simple knapsack problem and the knapsack problem. Four of them will be shown and proved in this paper.
Knapsack Problem
, 2004
"... We explain how the Knapsack problem and interactive rendering are related. We also discuss several additional concerns regarding interactive rendering and how these affect the solution to the original Knapsack problem. Lastly, we present two approximate algorithms and compare how they meet the needs ..."
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We explain how the Knapsack problem and interactive rendering are related. We also discuss several additional concerns regarding interactive rendering and how these affect the solution to the original Knapsack problem. Lastly, we present two approximate algorithms and compare how they meet
Algorithms for Knapsack Problems
, 1995
"... This thesis considers a family of combinatorial problems known under the name Knapsack Problems. As all the problems are A7)hard we are searching for exact solution techniques having reasonable solution times for nearly all instances encountered in practice, despite having exponential time bounds f ..."
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Cited by 95 (5 self)
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This thesis considers a family of combinatorial problems known under the name Knapsack Problems. As all the problems are A7)hard we are searching for exact solution techniques having reasonable solution times for nearly all instances encountered in practice, despite having exponential time bounds
The knapsack problem with neighbour constraints
 J. of Discrete Algorithms
, 2012
"... We study a constrained version of the knapsack problem in which dependencies between items are given by the adjacencies of a graph. In the 1neighbour knapsack problem, an item can be selected only if at least one of its neighbours is also selected. In the allneighbours knapsack problem, an item ca ..."
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Cited by 2 (0 self)
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We study a constrained version of the knapsack problem in which dependencies between items are given by the adjacencies of a graph. In the 1neighbour knapsack problem, an item can be selected only if at least one of its neighbours is also selected. In the allneighbours knapsack problem, an item
Where are the hard knapsack problems?
, 2003
"... The knapsack problem is believed to be one of the “easier” N Phard problems. Not only can it be solved in pseudopolynomial time, but also decades of algorithmic improvements have made it possible to solve nearly all standard instances from the literature. The purpose of this paper is to give an ov ..."
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Cited by 53 (2 self)
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The knapsack problem is believed to be one of the “easier” N Phard problems. Not only can it be solved in pseudopolynomial time, but also decades of algorithmic improvements have made it possible to solve nearly all standard instances from the literature. The purpose of this paper is to give
A nonlinear Knapsack Problem
 Operations Research Letters
, 1995
"... The nonlinear Knapsack problem is to maximize a separable concave objective function, subject to a single "packing" constraint, in nonnegative variables. We consider this problem in integer and continuous variables, and also when the packing constraint is convex. Although the nonlinear Kna ..."
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Cited by 12 (0 self)
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The nonlinear Knapsack problem is to maximize a separable concave objective function, subject to a single "packing" constraint, in nonnegative variables. We consider this problem in integer and continuous variables, and also when the packing constraint is convex. Although the nonlinear
The 1Neighbour Knapsack Problem
"... Abstract. We study a constrained version of the knapsack problem in which dependencies between items are given by the adjacencies of a graph. In the 1neighbour knapsack problem, an item can be selected only if at least one of its neighbours is also selected. We give approximation algorithms and har ..."
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Cited by 1 (0 self)
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Abstract. We study a constrained version of the knapsack problem in which dependencies between items are given by the adjacencies of a graph. In the 1neighbour knapsack problem, an item can be selected only if at least one of its neighbours is also selected. We give approximation algorithms
The Knapsack Problem with Conflict Graphs
, 2009
"... We extend the classical 01 knapsack problem by introducing disjunctive constraints for pairs of items which are not allowed to be packed together into the knapsack. These constraints are represented by edges of a conflict graph whose vertices correspond to the items of the knapsack problem. Similar ..."
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Cited by 6 (3 self)
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We extend the classical 01 knapsack problem by introducing disjunctive constraints for pairs of items which are not allowed to be packed together into the knapsack. These constraints are represented by edges of a conflict graph whose vertices correspond to the items of the knapsack problem
Factoring Polynomials and the Knapsack Problem.
"... Although a polynomial time algorithm exists, the most commonly used algorithm for factoring a univariate polynomial f with integer coefficients is the BerlekampZassenhaus algorithm which has a complexity that depends exponentially on n where n is the number of modular factors of f . This expone ..."
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Cited by 53 (15 self)
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. This exponential time complexity is due to a combinatorial problem; the problem of choosing the right subset of these n factors. In this paper we reduce this combinatorial problem to a knapsack problem of a kind that can be solved with polynomial time algorithms such LLL or PSLQ. The result is a practical
Statistical mechanics of the knapsack problem
, 1994
"... The knapsack problem is an NPcomplete combinatorial optimization problem with inequality constnints. Using the replica method of statistical physics, we study the space of its solutions for a large problem size. It turns out that this problem is closely related to the theory of the binary perceptro ..."
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The knapsack problem is an NPcomplete combinatorial optimization problem with inequality constnints. Using the replica method of statistical physics, we study the space of its solutions for a large problem size. It turns out that this problem is closely related to the theory of the binary
Results 1  10
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