Combinatorial optimization: algorithms and complexity
Combinatorial optimization: algorithms and complexity
Computers and Intractability: A Guide to the Theory of NP-Completeness
Computers and Intractability: A Guide to the Theory of NP-Completeness
Approximate minimization algorithms for the 0/1 Knapsack and Subset-Sum Problem
Operations Research Letters
Average-case analysis of a greedy algorithm for the 0/1 knapsack problem
Operations Research Letters
A novel multi-mutation binary particle swarm optimization for 0/1 knapsack problem
CCDC'09 Proceedings of the 21st annual international conference on Chinese control and decision conference
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A formal description of primal and dual greedy methods is given for a minimization version of the knapsack problem with Boolean variables. Relations of these methods to the corresponding methods for the maximization problem are shown. Average behavior of primal and dual methods for the minimization problem is studied. It is assumed that the coefficients of the objective function and the restriction are independent uniformly distributed on [0,1] random variables and that the right-hand side d is deterministic and proportional to the number of variables, i.e., d = μn. It is shown that for μ t/3 primal and dual greedy methods have an asymptotical accuracy t.