[2411.15282] Totally $Δ$-modular IPs with two non-zeros in most rows
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Computer Science > Data Structures and Algorithms

arXiv:2411.15282 (cs)
[Submitted on 22 Nov 2024]

Title:Totally $Δ$-modular IPs with two non-zeros in most rows

Authors:Stefan Kober
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Abstract:Integer programs (IPs) on constraint matrices with bounded subdeterminants are conjectured to be solvable in polynomial time. We give a strongly polynomial time algorithm to solve IPs where the constraint matrix has bounded subdeterminants and at most two non-zeros per row after removing a constant number of rows and columns. This result extends the work by Fiorini, Joret, Weltge \& Yuditsky (J. ACM 2024) by allowing for additional, unifying constraints and variables.
Subjects: Data Structures and Algorithms (cs.DS); Discrete Mathematics (cs.DM); Combinatorics (math.CO); Optimization and Control (math.OC)
Cite as: arXiv:2411.15282 [cs.DS]
  (or arXiv:2411.15282v1 [cs.DS] for this version)
  https://doi.org/10.48550/arXiv.2411.15282

Submission history

From: Stefan Kober [view email]
[v1] Fri, 22 Nov 2024 16:24:19 UTC (75 KB)
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