Unary Integer Linear Programming with Structural Restrictions

Kód výsledku v IS VaVaI

<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F00216208%3A11320%2F18%3A10387259" target="_blank" >RIV/00216208:11320/18:10387259 - isvavai.cz</a>

Nalezeny alternativní kódy

RIV/00216224:14330/18:00106814

Výsledek na webu

<a href="https://doi.org/10.24963/ijcai.2018/179" target="_blank" >https://doi.org/10.24963/ijcai.2018/179</a>

DOI - Digital Object Identifier

<a href="http://dx.doi.org/10.24963/ijcai.2018/179" target="_blank" >10.24963/ijcai.2018/179</a>

Jazyk výsledku

angličtina

Název v původním jazyce

Unary Integer Linear Programming with Structural Restrictions

Popis výsledku v původním jazyce

Recently a number of algorithmic results have appeared which show the tractability of Integer Linear Programming (ILP) instances under strong restrictions on variable domains and/or coefficients (AAAI 2016, AAAI 2017, IJCAI 2017). In this paper, we target ILPs where neither the variable domains nor the coefficients are restricted by a fixed constant or parameter; instead, we only require that our instances can be encoded in unary. We provide new algorithms and lower bounds for such ILPs by exploiting the structure of their variable interactions, represented as a graph. Our first set of results focuses on solving ILP instances through the use of a graph parameter called clique-width, which can be seen as an extension of treewidth which also captures well-structured dense graphs. In particular, we obtain a polynomial-time algorithm for instances of bounded clique-width whose domain and coefficients are polynomially bounded by the input size, and we complement this positive result by a number of algorithmic lower bounds. Afterwards, we turn our attention to ILPs with acyclic variable interactions. In this setting, we obtain a complexity map for the problem with respect to the graph representation used and restrictions on the encoding.

Název v anglickém jazyce

Unary Integer Linear Programming with Structural Restrictions

Popis výsledku anglicky

Recently a number of algorithmic results have appeared which show the tractability of Integer Linear Programming (ILP) instances under strong restrictions on variable domains and/or coefficients (AAAI 2016, AAAI 2017, IJCAI 2017). In this paper, we target ILPs where neither the variable domains nor the coefficients are restricted by a fixed constant or parameter; instead, we only require that our instances can be encoded in unary. We provide new algorithms and lower bounds for such ILPs by exploiting the structure of their variable interactions, represented as a graph. Our first set of results focuses on solving ILP instances through the use of a graph parameter called clique-width, which can be seen as an extension of treewidth which also captures well-structured dense graphs. In particular, we obtain a polynomial-time algorithm for instances of bounded clique-width whose domain and coefficients are polynomially bounded by the input size, and we complement this positive result by a number of algorithmic lower bounds. Afterwards, we turn our attention to ILPs with acyclic variable interactions. In this setting, we obtain a complexity map for the problem with respect to the graph representation used and restrictions on the encoding.

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

2018

Kód důvěrnosti údajů

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

Název statě ve sborníku

Proceedings of the Twenty-Seventh International Joint Conference on Artificial Intelligence

ISBN

978-0-9992411-2-7

ISSN

—

e-ISSN

neuvedeno

Počet stran výsledku

7

Strana od-do

1284-1290

Název nakladatele

International Joint Conferences on Artificial Intelligence

Místo vydání

Neuveden

Místo konání akce

Stockholm

Datum konání akce

13. 7. 2018

Typ akce podle státní příslušnosti

WRD - Celosvětová akce

Kód UT WoS článku

—