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

Kód výsledku v IS VaVaI

<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F00216208%3A11320%2F17%3A10366386" target="_blank" >RIV/00216208:11320/17:10366386 - isvavai.cz</a>

Nalezeny alternativní kódy

RIV/00216224:14330/17:00100548

Výsledek na webu

<a href="https://arxiv.org/abs/1706.06084" target="_blank" >https://arxiv.org/abs/1706.06084</a>

DOI - Digital Object Identifier

<a href="http://dx.doi.org/10.24963/ijcai.2017/85" target="_blank" >10.24963/ijcai.2017/85</a>

Jazyk výsledku

angličtina

Název v původním jazyce

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

Popis výsledku v původním jazyce

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 &apos;&apos;global&apos;&apos; 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.

Název v anglickém jazyce

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

Popis výsledku anglicky

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 &apos;&apos;global&apos;&apos; 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.

Druh

D - Stať ve sborníku

CEP obor

—

OECD FORD obor

10201 - Computer sciences, information science, bioinformathics (hardware development to be 2.2, social aspect to be 5.8)

Projekt

<a href="/cs/project/GBP202%2F12%2FG061" target="_blank" >GBP202/12/G061: Centrum excelence - Institut teoretické informatiky (CE-ITI)</a><br>

Návaznosti

P - Projekt vyzkumu a vyvoje financovany z verejnych zdroju (s odkazem do CEP)

Rok uplatnění

2017

Kód důvěrnosti údajů

S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

Název statě ve sborníku

Proceedings of the Twenty-Sixth International Joint Conference on Artificial Intelligence, IJCAI 2017, Melbourne, Australia, August 19-25, 2017

ISBN

978-0-9992411-0-3

ISSN

—

e-ISSN

neuvedeno

Počet stran výsledku

7

Strana od-do

607-613

Název nakladatele

ijcai.org

Místo vydání

Neuveden

Místo konání akce

Melbourne

Datum konání akce

19. 8. 2017

Typ akce podle státní příslušnosti

WRD - Celosvětová akce

Kód UT WoS článku

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