We study the standard-form ILP problem c^⊤ x → max Ax = b, x ∈ ℤ_{≥ 0}ⁿ, where A ∈ ℤ^{k× n} has full row rank. We obtain refined FPT algorithms parameterized by k and Δ, the maximum absolute value of a k× k minor of A. Our approach combines discrepancy-based dynamic programming with matrix discrepancy bounds in Komlós' setting. Let κ_k denote the maximum discrepancy over all matrices with k columns whose columns have Euclidean norm at most 1. Up to polynomial factors in the input size, the optimization problem can be solved in time O(κ_k)^{2k} Δ², and the corresponding feasibility problem in time O(κ_k)^kΔ. Using the best currently known bound κ_k = Õ(log^{1/4}k), this yields running times O(log k)^{k/2(1+o(1))} Δ² and O(log k)^{k/4(1+o(1))} Δ, respectively. Under the Komlós conjecture, the dependence on k in both running times reduces to 2^O(k).

In modern software development change-based testing plays a crucial role. However, as codebases expand and test suites grow, efficiently managing the testing process becomes increasingly challenging, especially given the high frequency of daily code commits. We propose Targeted Test Selection (T-TS), a machine learning approach for industrial test selection. Our key innovation is a data representation that represents commits as Bags-of-Words of changed files, incorporates cross-file and additional predictive features, and notably avoids the use of coverage maps. Deployed in production, T-TS was comprehensively evaluated against industry standards and recent methods using both internal and public datasets, measuring time efficiency and fault detection. On live industrial data, T-TS selects only$\mathbf{1 5} \%$of tests, reduces execution time by$5.9 \times$, accelerates the pipeline by$5.6 \times$, and detects over$\mathbf{9 5 \%}$of test failures. The implementation is publicly available to support further research and practical adoption.