MATRICES OF OPTIMAL TREE-DEPTH AND A ROW-INVARIANT PARAMETERIZED ALGORITHM FOR INTEGER PROGRAMMING

Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F00216208%3A11320%2F22%3A10455466" target="_blank" >RIV/00216208:11320/22:10455466 - isvavai.cz</a>
Alternative codes found
RIV/00216224:14330/22:00126436
Result on the web
<a href="https://verso.is.cuni.cz/pub/verso.fpl?fname=obd_publikace_handle&handle=OhD0NJ4S9" target="_blank" >https://verso.is.cuni.cz/pub/verso.fpl?fname=obd_publikace_handle&handle=OhD0NJ4S9</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.1137/20M1353502" target="_blank" >10.1137/20M1353502</a>

Result language
angličtina
Original language name
MATRICES OF OPTIMAL TREE-DEPTH AND A ROW-INVARIANT PARAMETERIZED ALGORITHM FOR INTEGER PROGRAMMING
Original language description
A long line of research on fixed parameter tractability of integer programming culminated with showing that integer programs with n variables and a constraint matrix with dual tree-depth d and largest entry Δ are solvable in time g(d, Δ )poly(n) for some function g. However, the dual tree-depth of a constraint matrix is not preserved by row operations, i.e., a given integer program can be equivalent to another with a smaller dual tree-depth, and thus does not reflect its geometric structure. We prove that the minimum dual tree-depth of a row-equivalent matrix is equal to the branch-depth of the matroid defined by the columns of the matrix. We design a fixed parameter algorithm for computing branch-depth of matroids represented over a finite field and a fixed parameter algorithm for computing a row-equivalent matrix with minimum dual treedepth. Finally, we use these results to obtain an algorithm for integer programming running in time g(dASTERISK OPERATOR, Δ )poly(n) where dASTERISK OPERATOR is the branch-depth of the constraint matrix; the branch-depth cannot be replaced by the more permissive notion of branch-width.
Czech name
—
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
<a href="/en/project/GX19-27871X" target="_blank" >GX19-27871X: Efficient approximation algorithms and circuit complexity</a><br>
Continuities
P - Projekt vyzkumu a vyvoje financovany z verejnych zdroju (s odkazem do CEP)

Publication year
2022
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

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