A note on the approximability of deepest-descent circuit steps

Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F00216208%3A11320%2F21%3A10437095" target="_blank" >RIV/00216208:11320/21:10437095 - isvavai.cz</a>
Result on the web
<a href="https://verso.is.cuni.cz/pub/verso.fpl?fname=obd_publikace_handle&handle=j9VRI5hDQE" target="_blank" >https://verso.is.cuni.cz/pub/verso.fpl?fname=obd_publikace_handle&handle=j9VRI5hDQE</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.1016/j.orl.2021.02.003" target="_blank" >10.1016/j.orl.2021.02.003</a>

Result language
angličtina
Original language name
A note on the approximability of deepest-descent circuit steps
Original language description
Linear programs (LPs) can be solved by polynomially many moves along the circuit direction improving the objective the most, so-called deepest-descent steps (dd-steps). Computing these steps is NP-hard (De Loera et al. (2019)), a consequence of the hardness of deciding the existence of an optimal circuit-neighbor (OCNP) on LPs with non-unique optima. We prove OCNP is easy under the promise of unique optima, but already O(n(1-epsilon))-approximating dd-steps remains hard even for totally unimodular n-dimensional 0/1-LPs with a unique optimum. We provide a matching n-approximation. (C) 2021 Elsevier B.V. All rights reserved.
Czech name
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Czech description
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Type
J<sub>imp</sub> - Article in a specialist periodical, which is included in the Web of Science database
CEP classification
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OECD FORD branch
10201 - Computer sciences, information science, bioinformathics (hardware development to be 2.2, social aspect to be 5.8)

Project
Result was created during the realization of more than one project. More information in the Projects tab.
Continuities
P - Projekt vyzkumu a vyvoje financovany z verejnych zdroju (s odkazem do CEP)

Publication year
2021
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

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