On a Simple Connection Between $$\Delta$$-Modular ILP and LP, and a New Bound on the Number of Integer Vertices-Reference-Cited by-同舟云学术

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On a Simple Connection Between $$\Delta$$-Modular ILP and LP, and a New Bound on the Number of Integer Vertices

Published:2024-04-04 Issue:2 Volume:5 Page:
ISSN:2662-2556
Container-title:Operations Research Forum
language:en
Short-container-title:Oper. Res. Forum

Author:

Gribanov Dmitry,Malyshev Dmitry,Shumilov Ivan

Funder

Russian Science Foundation,Russia

Publisher

Springer Science and Business Media LLC

Link

https://link.springer.com/content/pdf/10.1007/s43069-024-00310-2.pdf

Reference18 articles.

1. Gribanov VD, Malyshev SD, Pardalos MP, Veselov IS (2018) FPT-algorithms for some problems related to integer programming. J Comb Optim 35:1128–1146. https://doi.org/10.1007/s10878-018-0264-z

2. Gribanov VD, Shumilov AI, Malyshev SD, Pardalos MP (2022) On $$\delta$$-modular integer linear problems in the canonical form and equivalent problems. J Glob Optim. https://doi.org/10.1007/s10898-022-01165-9

3. McMullen P (1970) The maximum numbers of faces of a convex polytope. Mathematika 17(2):179–184. https://doi.org/10.1112/S0025579300002850

4. Grünbaum B (2011) Convex polytopes. Graduate Texts in Mathematics. Springer, New York

5. Veselov IS, Chirkov YA (2008) Some estimates for the number of vertices of integer polyhedra. J Appl Ind Math 2:591–604. https://doi.org/10.1134/S1990478908040157

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