Knapsack problems: algorithms and computer implementations
Knapsack problems: algorithms and computer implementations
A threshold of ln n for approximating set cover
Journal of the ACM (JACM)
Fast Approximation Algorithms for the Knapsack and Sum of Subset Problems
Journal of the ACM (JACM)
The budgeted maximum coverage problem
Information Processing Letters
Approximation algorithms
Polylogarithmic inapproximability
Proceedings of the thirty-fifth annual ACM symposium on Theory of computing
Partially ordered knapsack and applications to scheduling
Discrete Applied Mathematics
Maximizing submodular set functions subject to multiple linear constraints
SODA '09 Proceedings of the twentieth Annual ACM-SIAM Symposium on Discrete Algorithms
Non-monotone submodular maximization under matroid and knapsack constraints
Proceedings of the forty-first annual ACM symposium on Theory of computing
A note on maximizing a submodular set function subject to a knapsack constraint
Operations Research Letters
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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 1-neighbour knapsack problem, an item can be selected only if at least one of its neighbours is also selected. In the all-neighbours knapsack problem, an item can be selected only if all its neighbours are also selected. We give approximation algorithms and hardness results when the vertices have both uniform and arbitrary weight and profit functions, and when the dependency graph is directed and undirected.