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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 and 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, p.~1284-1290. ISBN~978-0-9992411-2-7. Available from: https://dx.doi.org/10.24963/ijcai.2018/179.
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