Solving Integer Linear Programs with a Small Number of Global
Variables		and Constraints

D 2017

Solving Integer Linear Programs with a Small Number of Global Variables and Constraints

DVORAK, Pavel, Eduard EIBEN, Robert GANIAN, Dusan KNOP, Sebastian ORDYNIAK et. al.

Základní údaje

Originální název

Solving Integer Linear Programs with a Small Number of Global Variables and Constraints

Autoři

DVORAK, Pavel (203 Česká republika), Eduard EIBEN (703 Slovensko), Robert GANIAN (203 Česká republika, garant, domácí), Dusan KNOP (203 Česká republika) a Sebastian ORDYNIAK (40 Rakousko)

Vydání

USA, Proceedings of the Twenty-Sixth International Joint Conference on Artificial Intelligence, {IJCAI} 2017, Melbourne, Australia, August 19-25, 2017, od s. 607-613, 7 s. 2017

Nakladatel

ijcai.org

Další údaje

Jazyk

angličtina

Typ výsledku

Stať ve sborníku

Obor

10200 1.2 Computer and information sciences

Stát vydavatele

Spojené státy

Utajení

není předmětem státního či obchodního tajemství

Forma vydání

elektronická verze "online"

Odkazy

URL

Kód RIV

RIV/00216224:14330/17:00100548

Organizační jednotka

Fakulta informatiky

ISBN

978-0-9992411-0-3

ISSN

DOI

http://dx.doi.org/10.24963/ijcai.2017/85

UT WoS

000764137500085

Klíčová slova anglicky

Integer Linear Programming; Backdoors; Parameterized Algorithms

Štítky

core_A, firank_1

Příznaky

Mezinárodní význam, Recenzováno

Změněno: 16. 5. 2022 15:49, Mgr. Michal Petr

Anotace

V originále

Integer Linear Programming (ILP) has a broad range of applications in various areas of artificial intelligence. Yet in spite of recent advances, we still lack a thorough understanding of which structural restrictions make ILP tractable. Here we study ILP instances consisting of a small number of ``global'' variables and/or constraints such that the remaining part of the instance consists of small and otherwise independent components; this is captured in terms of a structural measure we call fracture backdoors which generalizes, for instance, the well-studied class of N-fold ILP instances. Our main contributions can be divided into three parts. First, we formally develop fracture backdoors and obtain exact and approximation algorithms for computing these. Second, we exploit these backdoors to develop several new parameterized algorithms for ILP; the performance of these algorithms will naturally scale based on the number of global variables or constraints in the instance. Finally, we complement the developed algorithms with matching lower bounds. Altogether, our results paint a near-complete complexity landscape of ILP with respect to fracture backdoors.

Citovat

DVORAK, Pavel, Eduard EIBEN, Robert GANIAN, Dusan KNOP a Sebastian ORDYNIAK. Solving Integer Linear Programs with a Small Number of Global Variables and Constraints. Online. In Carles Sierra. Proceedings of the Twenty-Sixth International Joint Conference on Artificial Intelligence, {IJCAI} 2017, Melbourne, Australia, August 19-25, 2017. USA: ijcai.org, 2017, s. 607-613. ISBN 978-0-9992411-0-3. Dostupné z: https://dx.doi.org/10.24963/ijcai.2017/85.

@inproceedings{1414040,
   author = {Dvorak, Pavel and Eiben, Eduard and Ganian, Robert and Knop, Dusan and Ordyniak, Sebastian},
   address = {USA},
   booktitle = {Proceedings of the Twenty-Sixth International Joint Conference on Artificial Intelligence, {IJCAI} 2017, Melbourne, Australia, August 19-25, 2017},
   doi = {http://dx.doi.org/10.24963/ijcai.2017/85},
   editor = {Carles Sierra},
   keywords = {Integer Linear Programming; Backdoors; Parameterized Algorithms},
   howpublished = {elektronická verze "online"},
   language = {eng},
   location = {USA},
   isbn = {978-0-9992411-0-3},
   pages = {607-613},
   publisher = {ijcai.org},
   title = {Solving Integer Linear Programs with a Small Number of Global Variables and Constraints},
   url = {https://www.ijcai.org/proceedings/2017/85},
   year = {2017}
}

TY  - JOUR
ID  - 1414040
AU  - Dvorak, Pavel - Eiben, Eduard - Ganian, Robert - Knop, Dusan - Ordyniak, Sebastian
PY  - 2017
TI  - Solving Integer Linear Programs with a Small Number of Global Variables and Constraints
PB  - ijcai.org
CY  - USA
SN  - 9780999241103
KW  - Integer Linear Programming
KW  - Backdoors
KW  - Parameterized Algorithms
UR  - https://www.ijcai.org/proceedings/2017/85
L2  - https://www.ijcai.org/proceedings/2017/85
N2  - Integer Linear Programming (ILP) has a broad range of applications in various areas of artificial intelligence. Yet in spite of recent advances, we still lack a thorough understanding of which structural restrictions make ILP tractable. Here we study ILP instances consisting of a small number of ``global'' variables and/or constraints such that the remaining part of the instance consists of small and otherwise independent components; this is captured in terms of a structural measure we call fracture backdoors which generalizes, for instance, the well-studied class of N-fold ILP instances. Our main contributions can be divided into three parts. First, we formally develop fracture backdoors and obtain exact and approximation algorithms for computing these. Second, we exploit these backdoors to develop several new parameterized algorithms for ILP; the performance of these algorithms will naturally scale based on the number of global variables or constraints in the instance. Finally, we complement the developed algorithms with matching lower bounds. Altogether, our results paint a near-complete complexity landscape of ILP with respect to fracture backdoors.
ER  -

DVORAK, Pavel, Eduard EIBEN, Robert GANIAN, Dusan KNOP a Sebastian ORDYNIAK. Solving Integer Linear Programs with a Small Number of Global Variables and Constraints. Online. In Carles Sierra. \textit{Proceedings of the Twenty-Sixth International Joint Conference on Artificial Intelligence, $\{$IJCAI$\}$ 2017, Melbourne, Australia, August 19-25, 2017}. USA: ijcai.org, 2017, s.~607-613. ISBN~978-0-9992411-0-3. Dostupné z: https://dx.doi.org/10.24963/ijcai.2017/85.

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