Determining Sharp Proximity Bounds for Low Row Rank and -Modularity
Published Online:12 Feb 2026https://doi.org/10.1287/ijoo.2025.0068
References
- (2020) Distances to lattice points in knapsack polyhedra. Math. Programming 182(1–2):175–198.Google Scholar
- (2024) On the maximal number of columns of a δ-modular integer matrix: Bounds and computations. Math. Programming 206(1):61–89.Google Scholar
- (2021) Classification of triples of lattice polytopes with a given mixed volume. Discrete Comput. Geometry 66(1):165–202.Google Scholar
- (2016) The power of pyramid decomposition in Normaliz. J. Symbolic Comput. 74:513–536.Google Scholar
- (2023) Normaliz, version 3.10.1. Algorithms for rational cones and affine monoids. Accessed December 4, 2024, https://www.normaliz.uni-osnabrueck.de.Google Scholar
- (2022) Improving the Cook et al. proximity bound given integral valued constraints. Aardal K, Sanità L, eds. Proc. Internat. Conf. Integer Programming Combinatorial Optim. (Springer, Cham), 84–97.Google Scholar
- (2024) Proximity and flatness bounds for linear integer optimization. Math. Oper. Res. 49(4):2446–2467.Link, Google Scholar
- (1986) Sensitivity theorems in integer linear programming. Math. Programming 34(3):251–264. Google Scholar
- (2022) Proximity in concave integer quadratic programming. Math. Programming 194(1–2):871–900.Google Scholar
- (2020) Proximity results and faster algorithms for integer programming using the Steinitz lemma. ACM Trans. Algorithms 16(1):1–14.Google Scholar
- (1965) On the relation between integer and noninteger solutions to linear programs. Proc. Natl. Acad. Sci. USA 53(2):260–265.Google Scholar
- (2004) PALP: A package for analysing lattice polytopes with applications to toric geometry. Comput. Phys. Comm. 157(1):87–106.Google Scholar
- (2020) Improving proximity bounds using sparsity. Proc. 6th Internat. Sympos. Combinatorial Optim. (Springer, New York), 115–127.Google Scholar
- (2022) Polynomial upper bounds on the number of differing columns of Δ-modular integer programs. Math. Oper. Res. 48(4):2267–2286.Google Scholar
- (2020) The distributions of functions related to parametric integer optimization. SIAM J. Appl. Algebraic Geometry 4(3):422–440.Google Scholar
- (2020) Distances between optimal solutions of mixed-integer programs. Math. Programming 179(1–2):455–468.Google Scholar
- (1998) Theory of Linear and Integer Programming (John Wiley & Sons, New York).Google Scholar
- The SageMath Developers (2024) SageMath, the Sage Mathematics Software System (version 10.5). https://github.com/sagemath/sage.Google Scholar
- (2009) Integer program with bimodular matrix. Discrete Optim. 6(2):220–222.Google Scholar
- (1981) The b-hull of an integer program. Discrete Appl. Math. (1979) 3(3):193–201.Google Scholar
- (2020) On proximity for k-regular mixed-integer linear optimization. Le Thi HA, Le HM, Pham Dinh T, eds. Optimization of Complex Systems: Theory, Models, Algorithms and Applications (Springer International Publishing, Cham, Switzlerand), 438–447.Google Scholar

