scholarly journals The b ‐bibranching problem: TDI system, packing, and discrete convexity

Networks ◽  
2021 ◽  
Author(s):  
Kenjiro Takazawa
Keyword(s):  
Discrete Convexity

scholarly journals A ranking model for the greedy algorithm and discrete convexity

2010 ◽  
Vol 132 (1-2) ◽  
pp. 393-407 ◽  
Author(s):  
Ulrich Faigle ◽  
Walter Kern ◽  
Britta Peis
Keyword(s):  
Greedy Algorithm ◽  
Discrete Convexity ◽  
Ranking Model ◽  
The Greedy Algorithm

scholarly journals Greedy systems of linear inequalities and lexicographically optimal solutions

2019 ◽  
Vol 53 (5) ◽  
pp. 1929-1935
Author(s):  
Satoru Fujishige
Keyword(s):  
Convex Functions ◽  
Linear Inequalities ◽  
Convex Polyhedra ◽  
Optimal Solutions ◽  
Integral Points ◽  
System Of Linear Inequalities ◽  
Discrete Convexity ◽  
The Greedy Algorithm

The present note reveals the role of the concept of greedy system of linear inequalities played in connection with lexicographically optimal solutions on convex polyhedra and discrete convexity. The lexicographically optimal solutions on convex polyhedra represented by a greedy system of linear inequalities can be obtained by a greedy procedure, a special form of which is the greedy algorithm of J. Edmonds for polymatroids. We also examine when the lexicographically optimal solutions become integral. By means of the Fourier–Motzkin elimination Murota and Tamura have recently shown the existence of integral points in a polyhedron arising as a subdifferential of an integer-valued, integrally convex function due to Favati and Tardella [Murota and Tamura, Integrality of subgradients and biconjugates of integrally convex functions. Preprint arXiv:1806.00992v1 (2018)], which can be explained by our present result. A characterization of integrally convex functions is also given.

Discrete Convexity, Straightness, and the 16-Neighborhood

1997 ◽  
Vol 66 (3) ◽  
pp. 316-329 ◽  
Author(s):  
Stéphane Marchand-Maillet ◽  
Yazid M Sharaiha
Keyword(s):  
Discrete Convexity

scholarly journals Separation of integer points by a hyperplane under some weak notions of discrete convexity

2013 ◽  
Vol 313 (1) ◽  
pp. 8-18
Author(s):  
Takuya Kashimura ◽  
Yasuhide Numata ◽  
Akimichi Takemura
Keyword(s):  
Integer Points ◽  
Discrete Convexity

scholarly journals Detection of the discrete convexity of polyominoes

2003 ◽  
Vol 125 (1) ◽  
pp. 115-133 ◽  
Author(s):  
Isabelle Debled-Rennesson ◽  
Jean-Luc Rémy ◽  
Jocelyne Rouyer-Degli
Keyword(s):  
Discrete Convexity

scholarly journals Classes of Discrete Convexity Properties

2004 ◽  
Vol 31 (3) ◽  
pp. 461-490 ◽  
Author(s):  
Gabriela Cristescu ◽  
Liana Lupsa
Keyword(s):  
Discrete Convexity ◽  
Convexity Properties

Discrete convexity and its characterization via the fractional Hermite–Hadamard inequality

Analysis ◽  
2017 ◽  
Vol 37 (3) ◽  
Author(s):  
Aykut Arslan
Keyword(s):  
Hadamard Inequality ◽  
Discrete Convexity

AbstractIn this paper, we obtain the fractional Hermite–Hadamard inequality on

scholarly journals Convexity in Ordered Matroids and the Generalized External Order

10.37236/7582 ◽  
2020 ◽  
Vol 27 (3) ◽  
Author(s):  
Bryan R. Gillespie
Keyword(s):  
Distributive Lattice ◽  
Generating Function ◽  
Convex Sets ◽  
Convex Geometry ◽  
Tutte Polynomial ◽  
Oriented Matroids ◽  
Geometric Lattice ◽  
Discrete Convexity ◽  
New Type ◽  
Convex Geometries

In 1980, Las Vergnas defined a notion of discrete convexity for oriented matroids, which Edelman subsequently related to the theory of anti-exchange closure functions and convex geometries. In this paper, we use generalized matroid activity to construct a convex geometry associated with an ordered, unoriented matroid. The construction in particular yields a new type of representability for an ordered matroid defined by the affine representability of its corresponding convex geometry. The lattice of convex sets of this convex geometry induces an ordering on the matroid independent sets which extends the external active order on matroid bases. We show that this generalized external order forms a supersolvable meet-distributive lattice refining the geometric lattice of flats, and we uniquely characterize the lattices isomorphic to the external order of a matroid. Finally, we introduce a new trivariate generating function generalizing the matroid Tutte polynomial.

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