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Geometry of numbers and integer programming

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What this work says

Outgoing claims: the papers this work cites, builds on, or argues with.

inferredcites →https://doi.org/10.1007/3-540-13345-3_40openalex-snapshot

Factorization of univariate integer polynomials by diophantine approximation and an improved basis reduction algorithm

inferredcites →https://doi.org/10.1007/3-540-16078-7_69openalex-snapshot

Polynomial time algorithms for finding integer relations among real numbers

inferredcites →https://doi.org/10.1007/978-3-0348-5765-9_7openalex-snapshot

Geometry of Numbers

inferredcites →https://doi.org/10.1007/978-3-642-62035-5openalex-snapshot

An Introduction to the Geometry of Numbers

inferredcites →https://doi.org/10.1007/bf01442795openalex-snapshot

Sur les formes quadratiques

inferredcites →https://doi.org/10.1007/bf01449880openalex-snapshot

Grundlagen f�r eine Theorie des Jacobischen Kettenbruchalgorithmus

inferredcites →https://doi.org/10.1007/bf01457454openalex-snapshot

Factoring polynomials with rational coefficients

inferredcites →https://doi.org/10.1007/bf02579403openalex-snapshot

On Lovász’ lattice reduction and the nearest lattice point problem

inferredcites →https://doi.org/10.1007/bfb0023990openalex-snapshot

On Lovász' lattice reduction and the nearest lattice point problem

inferredcites →https://doi.org/10.1016/0304-3975(85)90067-2openalex-snapshot

Algorithms to construct minkowski reduced and hermite reduced lattice bases

inferredcites →https://doi.org/10.1016/0304-3975(87)90064-8openalex-snapshot

A hierarchy of polynomial time lattice basis reduction algorithms

inferredcites →https://doi.org/10.1090/s0273-0979-1979-14691-3openalex-snapshot

Generalization of the Euclidean algorithm for real numbers to all dimensions higher than two

inferredcites →https://doi.org/10.1109/sfcs.1983.70openalex-snapshot

Solving low density subset sum problems

inferredcites →https://doi.org/10.1109/sfcs.1984.715950openalex-snapshot

Linear Congruential Generators Do Not Produce Random Sequences

inferredcites →https://doi.org/10.1137/0218059openalex-snapshot

Polynomial Time Algorithms for Finding Integer Relations among Real Numbers

inferredcites →https://doi.org/10.1287/moor.12.3.415openalex-snapshot

Minkowski's Convex Body Theorem and Integer Programming

inferredcites →https://doi.org/10.1287/moor.8.4.538openalex-snapshot

Integer Programming with a Fixed Number of Variables

inferredcites →https://doi.org/10.14463/gbv:1014770351openalex-snapshot

Geometrie der Zahlen

inferredcites →https://doi.org/10.1515/crll.1868.69.29openalex-snapshot

Allgemeine Theorie der kettenbruchähnlichen Algorithmen, in welchen jede Zahl aus drei vorhergehenden gebildet wird.

What points at this work

Incoming claims: where this work appears in other papers’ reference lists and arguments.

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An integer lattice arising in the model theory of wreath products

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Intersection Cuts for Polynomial Optimization

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On the Unique-Lifting Property

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Linear Inequalities and Polyhedra

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Intersection Cuts and Corner Polyhedra

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Valid Inequalities for Structured Integer Programs

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Reformulations and Relaxations

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Mixed-Integer Convex Representability

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Approximation of Corner Polyhedra with Families of Intersection Cuts

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The Group-Theoretic Approach in Mixed Integer Programming

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Computing with Multi-row Gomory Cuts

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On the Facets of Mixed Integer Programs with Two Integer Variables and Two Constraints

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Building Bridges

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Experiments with Two Row Tableau Cuts

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Test sets of integer programs

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Lattice translates of a polytope and the Frobenius problem

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The topological structure of maximal lattice free convex bodies: The general case

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The Covering Radius and a Discrete Surface Area for Non-Hollow Simplices

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Two row mixed-integer cuts via lifting

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Mixed-integer sets from two rows of two adjacent simplex bases

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Two dimensional lattice-free cuts and asymmetric disjunctions for mixed-integer polyhedra

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Generalized intersection cuts and a new cut generating paradigm

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Some properties of convex hulls of integer points contained in general convex sets

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Unbounded convex sets for non-convex mixed-integer quadratic programming

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The triangle closure is a polyhedron

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Lattice-free sets, multi-branch split disjunctions, and mixed-integer programming

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Lifting properties of maximal lattice-free polyhedra

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Intersection cuts for nonlinear integer programming: convexification techniques for structured sets

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Reverse split rank

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Duality for mixed-integer convex minimization

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On the relationship between standard intersection cuts, lift-and-project cuts, and generalized intersection cuts

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Theoretical challenges towards cutting-plane selection

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Lattice closures of polyhedra

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Outer-product-free sets for polynomial optimization and oracle-based cuts

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Constructing lattice-free gradient polyhedra in dimension two

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Relaxations of mixed integer sets from lattice-free polyhedra

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Relaxations of mixed integer sets from lattice-free polyhedra

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Intersection cuts for single row corner relaxations

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Inequalities for the lattice width of lattice-free convex sets in the plane

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Convexity and Discrete Optimization

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Tight bounds on discrete quantitative Helly numbers

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Largest integral simplices with one interior integral point: Solution of Hensley's conjecture and related results

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A local maximizer for lattice width of 3-dimensional hollow bodies

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Strengthening lattice-free cuts using non-negativity

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On finitely generated closures in the theory of cutting planes

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Certificates of linear mixed integer infeasibility

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Computing with multi-row Gomory cuts

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Equivalence between intersection cuts and the corner polyhedron

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A probabilistic comparison of the strength of split, triangle, and quadrilateral cuts

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Corner polyhedron and intersection cuts

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The Structure of Group Relaxations

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Block Reduced Lattice Bases and Successive Minima

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The Generalized Basis Reduction Algorithm

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Matrices with Identical Sets of Neighbors

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The Frobenius Problem and Maximal Lattice Free Bodies

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Helly’s theorem: New variations and applications

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Reducing lattice bases with Bergman exchange

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Lattice reduced and complete convex bodies

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Constrained Infinite Group Relaxations of MIPs

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Minimal Inequalities for an Infinite Relaxation of Integer Programs

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On Maximal S -Free Convex Sets

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A Probabilistic Comparison of Split and Type 1 Triangle Cuts for Two-Row Mixed-Integer Programs

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A Strong Dual for Conic Mixed-Integer Programs

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Operations that Preserve the Covering Property of the Lifting Region

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Maximal $S$-Free Convex Sets and the Helly Number

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Sublinear Bounds for a Quantitative Doignon--Bell--Scarf Theorem

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Can Cut-Generating Functions Be Good and Efficient?

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A Cutting Plane Theory for Mixed Integer Optimization

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Solution of the Frobenius problem

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Intersection Cuts with Infinite Split Rank

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Experiments with Two-Row Cuts from Degenerate Tableaux

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On the Practical Strength of Two-Row Tableau Cuts

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Minimal Valid Inequalities for Integer Constraints

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The Generalized Basis Reduction Algorithm

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Cut-Generating Functions and S -Free Sets

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Mixed-Integer Convex Representability

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The associated primes of initial ideals of lattice ideals

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A probabilistic comparison of the strength of split, triangle, and quadrilateral cuts (extended version)

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A proof of Lovász's theorem on maximal lattice-free sets

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Improved theoretical guarantees regarding a class of two-row cutting planes

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Reverse Chvátal-Gomory rank

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Existence of sublattice points in lattice polygons

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Bounds on the number of vertices of sublattice-free lattice polygons

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Valid inequalities for mixed-integer linear programming problems

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