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Mathematics > Combinatorics

arXiv:2108.03616 (math)
[Submitted on 8 Aug 2021 (v1), last revised 14 Dec 2021 (this version, v2)]

Title:Circuit imbalance measures and linear programming

Authors:Farbod Ekbatani, Bento Natura, László A. Végh
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Abstract:We study properties and applications of various circuit imbalance measures associated with linear spaces. These measures describe possible ratios between nonzero entries of support-minimal nonzero vectors of the space. The fractional circuit imbalance measure turns out to be a crucial parameter in the context of linear programming, and two integer variants can be used to describe integrality properties of associated polyhedra.
We give an overview of the properties of these measures, and survey classical and recent applications, in particular, for linear programming algorithms with running time dependence on the constraint matrix only, and for circuit augmentation algorithms. We also present new bounds on the diameter and circuit diameter of polyhedra in terms of the fractional circuit imbalance measure.
Subjects: Combinatorics (math.CO); Discrete Mathematics (cs.DM); Data Structures and Algorithms (cs.DS); Optimization and Control (math.OC)
Cite as: arXiv:2108.03616 [math.CO]
  (or arXiv:2108.03616v2 [math.CO] for this version)
  https://doi.org/10.48550/arXiv.2108.03616

Submission history

From: Bento Natura [view email]
[v1] Sun, 8 Aug 2021 11:55:34 UTC (52 KB)
[v2] Tue, 14 Dec 2021 17:56:54 UTC (73 KB)
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