Theory of linear and integer programming
Theory of linear and integer programming
Integer and combinatorial optimization
Integer and combinatorial optimization
Introduction to algorithms
Knapsack problems: algorithms and computer implementations
Knapsack problems: algorithms and computer implementations
Approximation schemes for the restricted shortest path problem
Mathematics of Operations Research
Improved approximations of packing and covering problems
STOC '95 Proceedings of the twenty-seventh annual ACM symposium on Theory of computing
On multi-dimensional packing problems
Proceedings of the tenth annual ACM-SIAM symposium on Discrete algorithms
On the complexity of integer programming
Journal of the ACM (JACM)
A PTAS for the multiple knapsack problem
SODA '00 Proceedings of the eleventh annual ACM-SIAM symposium on Discrete algorithms
Dynamic Programming and Optimal Control
Dynamic Programming and Optimal Control
Introduction to Algorithms: A Creative Approach
Introduction to Algorithms: A Creative Approach
Computers and Intractability: A Guide to the Theory of NP-Completeness
Computers and Intractability: A Guide to the Theory of NP-Completeness
A Genetic Algorithm for the Multidimensional Knapsack Problem
Journal of Heuristics
Generalized Assignment Problems
ISAAC '92 Proceedings of the Third International Symposium on Algorithms and Computation
On the Approximability of Interactive Knapsack Problems
SOFSEM '01 Proceedings of the 28th Conference on Current Trends in Theory and Practice of Informatics Piestany: Theory and Practice of Informatics
Resource Scheduling in Enhanced Pay-Per-View Continuous Media Databases
VLDB '97 Proceedings of the 23rd International Conference on Very Large Data Bases
Fundamenta Informaticae
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We describe a special case of the interactive knapsack optimization problem (motivated by the load clipping problem) solvable in polynomial time. Given an instance parameterized by k , the solution can be found in polynomial time, where the polynomial has degree k . In the interactive knapsack problem, k is connected to the length induced by an item. A similar construction solves a special case of the 0-1 multi-dimensional knapsack and the 0-1 linear integer programming problems in polynomial time. In these problems the parameter determines the width of the restriction matrix, which is a band matrix. We extend the 0-1 multi-dimensional knapsack solution to 0- n multi-dimensional knapsack problems (and to 0- n IP problems). Our algorithms are based on the (resource bounded) shortest path search: we represent restrictions efficiently in a form of a graph such that each feasible solution has a path between given source and target vertices.