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On circuit diameter bounds via circuit imbalances

Dadush, Daniel, Koh, Zhuan Khye, Natura, Bento and Végh, László A A. ORCID: 0000-0003-1152-200X (2022) On circuit diameter bounds via circuit imbalances. In: Aardal, Karen and Sanità, Laura, (eds.) Integer Programming and Combinatorial Optimization - 23rd International Conference, IPCO 2022, Proceedings. Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics),13265. Springer Science and Business Media Deutschland GmbH, 140 - 153. ISBN 9783031069000

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Identification Number: 10.1007/978-3-031-06901-7_11

Abstract

We study the circuit diameter of polyhedra, introduced by Borgwardt, Finhold, and Hemmecke (SIDMA 2015) as a relaxation of the combinatorial diameter. We show that the circuit diameter of a system {x∈Rn:Ax=b,0≤x≤u} for A∈ Rm × n is bounded by O(m2log (m+ κA) + nlog n), where κA is the circuit imbalance measure of the constraint matrix. This yields a strongly polynomial circuit diameter bound if e.g., all entries of A have polynomially bounded encoding length in n. Further, we present circuit augmentation algorithms for LPs using the minimum-ratio circuit cancelling rule. Even though the standard minimum-ratio circuit cancelling algorithm is not finite in general, our variant can solve an LP in O(n3log (n+ κA) ) augmentation steps.

Item Type: Book Section
Official URL: https://link.springer.com/book/10.1007/978-3-031-0...
Additional Information: © 2022 Springer Nature Switzerland AG.
Divisions: Statistics
Mathematics
Subjects: Q Science > QA Mathematics > QA75 Electronic computers. Computer science
Date Deposited: 22 Jul 2022 17:09
Last Modified: 07 Nov 2022 10:45
URI: http://eprints.lse.ac.uk/id/eprint/115640

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