Matrices of optimal tree-depth and a row-invariant parameterized algorithm for integer programming
The result's identifiers
Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F00216224%3A14330%2F20%3A00116613" target="_blank" >RIV/00216224:14330/20:00116613 - isvavai.cz</a>
Result on the web
<a href="http://dx.doi.org/10.4230/LIPIcs.ICALP.2020.26" target="_blank" >http://dx.doi.org/10.4230/LIPIcs.ICALP.2020.26</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.4230/LIPIcs.ICALP.2020.26" target="_blank" >10.4230/LIPIcs.ICALP.2020.26</a>
Alternative languages
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 D are solvable in time g(d,D)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 tree-depth. Finally, we use these results to obtain an algorithm for integer programming running in time g(d*,D)poly(n) where d* is the branch-depth of the constraint matrix; the branch-depth cannot be replaced by the more permissive notion of branch-width.
Czech name
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Czech description
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Classification
Type
D - Article in proceedings
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)
Result continuities
Project
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Continuities
I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace
Others
Publication year
2020
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů
Data specific for result type
Article name in the collection
Proceedings of the 47th International Colloquium on Automata, Languages, and Programming (ICALP 2020), p. "26:1"-"26:19", 19 pp. 2020.
ISBN
9783959771382
ISSN
1868-8969
e-ISSN
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Number of pages
19
Pages from-to
„26:1“-„26:19“
Publisher name
Schloss Dagstuhl--Leibniz-Zentrum fuer Informatik
Place of publication
Dagstuhl, Germany
Event location
Dagstuhl, Germany
Event date
Jan 1, 2020
Type of event by nationality
WRD - Celosvětová akce
UT code for WoS article
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