We study the complexity of the 2-dimensional knapsack problemmax{c_1 x + c_2 y : a_1 x + a_2 y <= b; x, y \in Z_+}, where c_1, c_2, a_1, a_2, b \in R_+. The problem is defined in terms of real numbers and we study it where an integral solution is sought under a real number model of computation. Weobtain a tight complexity bound Theta(log b/a_min), where a_min = min{a_1, a_2}.
Tight Complexity Bounds for the Two-Dimensional Real Knapsack / V. E., Brimkov; S. S., Danchev; Leoncini, Mauro. - In: CALCOLO. - ISSN 0008-0624. - STAMPA. - 36:(1999), pp. 123-128.
Tight Complexity Bounds for the Two-Dimensional Real Knapsack
LEONCINI, Mauro
1999
Abstract
We study the complexity of the 2-dimensional knapsack problemmax{c_1 x + c_2 y : a_1 x + a_2 y <= b; x, y \in Z_+}, where c_1, c_2, a_1, a_2, b \in R_+. The problem is defined in terms of real numbers and we study it where an integral solution is sought under a real number model of computation. Weobtain a tight complexity bound Theta(log b/a_min), where a_min = min{a_1, a_2}.
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