Feasibility of Integer Knapsacks
نویسندگان
چکیده
FEASIBILITY OF INTEGER KNAPSACKS∗ ISKANDER ALIEV† AND MARTIN HENK‡ Abstract. Given a matrix A ∈ Zm×n satisfying certain regularity assumptions, we consider the set F(A) of all vectors b ∈ Zm such that the associated knapsack polytope P (A, b) = {x ∈ R≥0 : Ax = b} contains an integer point. When m = 1 the set F(A) is known to contain all consecutive integers greater than the Frobenius number associated with A. In this paper we introduce the diagonal Frobenius number g(A) which reflects in an analogous way feasibility properties of the problem and the structure of F(A) in the general case. We give an optimal upper bound for g(A) and also estimate the asymptotic growth of the diagonal Frobenius number on average.
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عنوان ژورنال:
- SIAM Journal on Optimization
دوره 20 شماره
صفحات -
تاریخ انتشار 2010