تقرير
Tight Lower Bounds for Problems Parameterized by Rank-width
| العنوان: | Tight Lower Bounds for Problems Parameterized by Rank-width |
|---|---|
| المؤلفون: | Bergougnoux, Benjamin, Korhonen, Tuukka, Nederlof, Jesper |
| سنة النشر: | 2022 |
| المجموعة: | Computer Science |
| مصطلحات موضوعية: | Computer Science - Data Structures and Algorithms, 68Q27 |
| الوصف: | We show that there is no $2^{o(k^2)} n^{O(1)}$ time algorithm for Independent Set on $n$-vertex graphs with rank-width $k$, unless the Exponential Time Hypothesis (ETH) fails. Our lower bound matches the $2^{O(k^2)} n^{O(1)}$ time algorithm given by Bui-Xuan, Telle, and Vatshelle [Discret. Appl. Math., 2010] and it answers the open question of Bergougnoux and Kant\'{e} [SIAM J. Discret. Math., 2021]. We also show that the known $2^{O(k^2)} n^{O(1)}$ time algorithms for Weighted Dominating Set, Maximum Induced Matching and Feedback Vertex Set parameterized by rank-width $k$ are optimal assuming ETH. Our results are the first tight ETH lower bounds parameterized by rank-width that do not follow directly from lower bounds for $n$-vertex graphs. Comment: Accepted to STACS'23 |
| نوع الوثيقة: | Working Paper |
| URL الوصول: | http://arxiv.org/abs/2210.02117 |
| رقم الأكسشن: | edsarx.2210.02117 |
| قاعدة البيانات: | arXiv |
| الوصف غير متاح. |