2018
Unary Integer Linear Programming with Structural Restrictions
EIBEN, Eduard, Robert GANIAN, Dusan KNOP a Sebastian ORDYNIAKZákladní údaje
Originální název
Unary Integer Linear Programming with Structural Restrictions
Autoři
EIBEN, Eduard (703 Slovensko), Robert GANIAN (203 Česká republika, garant, domácí), Dusan KNOP (203 Česká republika) a Sebastian ORDYNIAK (276 Německo)
Vydání
USA, Proceedings of the Twenty-Seventh International Joint Conference on Artificial Intelligence, od s. 1284-1290, 7 s. 2018
Nakladatel
ijcai.org
Další údaje
Jazyk
angličtina
Typ výsledku
Stať ve sborníku
Obor
10201 Computer sciences, information science, bioinformatics
Stát vydavatele
Spojené státy
Utajení
není předmětem státního či obchodního tajemství
Forma vydání
elektronická verze "online"
Kód RIV
RIV/00216224:14330/18:00106814
Organizační jednotka
Fakulta informatiky
ISBN
978-0-9992411-2-7
ISSN
UT WoS
000764175401059
Klíčová slova anglicky
Integer Linear Programming; Classical Complexity
Příznaky
Mezinárodní význam, Recenzováno
Změněno: 18. 5. 2022 10:34, Mgr. Michal Petr
Anotace
V originále
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.