Author

Robert Hildebrand

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Preprint Sep 2026

Integer Maximization over $\ell_p$ Balls: Hardness and Exact Algorithms

We study the problem of maximizing a linear function over the integer points of an origin-centered $\ell_p$ ball, which we call \BallIPp{p}. For every fixed integer $p\ge2$, we prove that the decision problem over an $\ell_p$-ball is NP-complete. We then focus on the Euclidean case and study how the difficulty of the p...

Cinar Ari, Robert Hildebrand · 0 citations

Preprint Sep 2026

Bounded Integer Quadratic Programming through Parallelepiped Covers and Discrete Convic Optimization

We give an exact algorithm for minimizing an arbitrary rational quadratic polynomial $x^T Q x + c^T x + \gamma$ over the integer points of a bounded rational polyhedron $\{x : Ax \le b\}$. For $n$ variables and $m$ inequalities, the running time is $$2^{O(n \log(n+1))} (m+1)^{O(n)} \beta^{O(n)} (1+L)^{O(1)},$$ where $\...

Cinar Ari, Robert Hildebrand · 0 citations