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@inproceedings{1523777,
author = {Eiben, Eduard and Ganian, Robert and Knop, Dusan and Ordyniak, Sebastian},
address = {USA},
booktitle = {Proceedings of the Twenty-Seventh International Joint Conference on Artificial Intelligence},
doi = {http://dx.doi.org/10.24963/ijcai.2018/179},
editor = {Jerome Lang},
keywords = {Integer Linear Programming; Classical Complexity},
howpublished = {elektronická verze "online"},
language = {eng},
location = {USA},
isbn = {978-0-9992411-2-7},
pages = {1284-1290},
publisher = {ijcai.org},
title = {Unary Integer Linear Programming with Structural Restrictions},
year = {2018}
}
TY - JOUR
ID - 1523777
AU - Eiben, Eduard - Ganian, Robert - Knop, Dusan - Ordyniak, Sebastian
PY - 2018
TI - Unary Integer Linear Programming with Structural Restrictions
PB - ijcai.org
CY - USA
SN - 9780999241127
KW - Integer Linear Programming
KW - Classical Complexity
N2 - 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.
ER -
EIBEN, Eduard, Robert GANIAN, Dusan KNOP a Sebastian ORDYNIAK. Unary Integer Linear Programming with Structural Restrictions. Online. In Jerome Lang. \textit{Proceedings of the Twenty-Seventh International Joint Conference on Artificial Intelligence}. USA: ijcai.org, 2018, s.~1284-1290. ISBN~978-0-9992411-2-7. Dostupné z: https://dx.doi.org/10.24963/ijcai.2018/179.
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