Fair integral submodular flows

Integer-valued elements of an integral submodular flow polyhedron Q are investigated which are decreasingly minimal (dec-min) in the sense that their largest component is as small as possible, within this, the second largest component is as small as possible, and so on. As a main result, we prove th...

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Bibliographic Details
Published in:Discrete Applied Mathematics Vol. 320; pp. 416 - 434
Main Authors: Frank, András, Murota, Kazuo
Format: Journal Article
Language:English
Published: Elsevier B.V 30.10.2022
Subjects:
Fair optimization
Integral submodular flow
Polyhedral description
Polynomial algorithm
Polyhedral description
Fair optimization
Integral submodular flow
Polynomial algorithm
ISSN:0166-218X, 1872-6771
Online Access:Get full text
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Summary:Integer-valued elements of an integral submodular flow polyhedron Q are investigated which are decreasingly minimal (dec-min) in the sense that their largest component is as small as possible, within this, the second largest component is as small as possible, and so on. As a main result, we prove that the set of dec-min integral elements of Q is the set of integral elements of another integral submodular flow polyhedron arising from Q by intersecting a face of Q with a box. Based on this description, we develop a strongly polynomial algorithm for computing not only a dec-min integer-valued submodular flow but even a cheapest one with respect to a linear cost-function. A special case is the problem of finding a strongly connected (or k-edge-connected) orientation of a mixed graph whose in-degree vector is decreasingly minimal.
ISSN:0166-218X
1872-6771
DOI:10.1016/j.dam.2022.06.015