Hard Knapsack Problems

Vasek Chvátal
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Vasek Chvátal: McGill University, Montreal, Canada

Operations Research, 1980, vol. 28, issue 6, 1402-1411

Abstract: We consider a class of algorithms which use the combined powers of branch-and-bound, dynamic programming and rudimentary divisibility arguments for solving the zero-one knapsack problem. Our main result identifies a class of instances of the problem which are difficult to solve by such algorithms. More precisely, if reading the data takes t units of time, then the time required to solve the problem grows exponentially with the square root of t .

Date: 1980
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