The Support of Integer Optimal Solutions -- Talk by Timm Oertel Event

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The support of a vector is the number of nonzero-components. We show that given an integral m x n matrix A, the integer linear optimization problem max{ c^Tx : Ax = b, x>=0, x in Z^n} has an optimal solution whose support is bounded by 2m log(2 sqrt(m) ||A||), where ||A|| is the largest absolute value of an entry of A. Compared to previous bounds, the one presented here is independent on the objective function. We furthermore provide a nearly matching asymptotic lower bound on the support of optimal solutions.