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| teaching:intro_par_alg2324 [2023/10/11 16:05] – Tung Anh Vu | teaching:intro_par_alg2324 [2024/01/11 17:54] (aktuální) – lecture 11. 1. Martin Koutecky |
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| [[https://kam.mff.cuni.cz/~tung/teaching/fpt-ws2324/|Click here for the website of the tutorials]], where | [[https://kam.mff.cuni.cz/~tung/teaching/fpt-ws2324/|Click here for the website of the tutorials]], where |
| you can find materials from the tutorial sessions and instructions on how to solve homework. | you can find materials from the tutorial sessions and instructions on how to solve homework. |
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| | {{tablelayout?colwidth="100px,-"&rowsHeaderSource=1&rowsVisible=100&float=left}} |
| | ^ date ^ what was said [source] ^ |
| | | 5. 10. | Introduction to parameterized algorithms / complexity. **[PA 1]**| |
| | | 12. 10. | Kernelization **[PA 2.1, 2.2.1, 2.3-intro, 2.3.1, 2.5 without Lemma 2.22]**| |
| | | 19. 10. | Finishing kernels from last time. Bounded Search Trees: <typo fv:small-caps>Vertex Cover</typo> in $\mathcal{O}^*(1.6181^k)$ and $\mathcal{O}^*(1.4656^k)$ time; <typo fv:small-caps>Closest String</typo> in $\mathcal{O}^*(d^d)$ time **[PA 3.1, 3.5]**| |
| | | 26. 10. | FPT algorithm for <typo fv:small-caps>Vertex Cover above LP</typo>, application: FPT algorithm for <typo fv:small-caps>Odd Cycle Transversal</typo> **[PA 3.4]**; | |
| | | 2. 11. | **No class: [[https://www.mff.cuni.cz/en/internal-affairs/dean-s-day/2023|Dean's sport day]]**| |
| | | 9. 11. | Iterative Compression for <typo fv:small-caps>Vertex Cover</typo>, <typo fv:small-caps>Feedback Vertex Set</typo> and <typo fv:small-caps>Odd Cycle Transversal</typo>, **[PA 4.1, 4.3.1, 4.4]** | |
| | | 16. 11. | Dynamic programming and convolutions on <typo fv:small-caps>Set Cover</typo> and <typo fv:small-caps>Steiner Tree</typo> **[PA 6.1]**, PIE and <typo fv:small-caps>Hamiltonian Cycle</typo> **[PA 10.1.1]** | |
| | | 23. 11. | Treewidth, nice tree decompositions, <typo fv:small-caps>Independent Set</typo> **[PA 7.2, 7.3.1]**| |
| | | 30. 11. | More Treewidth - FPT alg., MSO, grids **[PA 7.7.1, 7.7.2 ]**| |
| | | 7. 12. | Intro to neighborhood diversity and ILPs. Solving <typo fv:small-caps>Coloring</typo> on graphs of bounded $nd(G)$. **[ND, NdCol, 5M]**| |
| | | 14. 12. | Neighborhood diversity: <typo fv:small-caps>Sum Coloring</typo> via $n$-fold IP, and as a convex IP in small dimension **[5M, Thm 2(a), 2(b)]**| |
| | | 21. 12. | Neighborhood diversity: finish <typo fv:small-caps>Sum Coloring</typo> **[5M, Thm 2]**, <typo fv:small-caps>Capacitated Dominating Set</typo> **[5M, Thm 1]**| |
| | | 4. 1. | Parameterized reductions, The W-hierarchy **[PA, 13.1, 13.2, 13.3]**| |
| | | 11. 1. | $P||C_{\max}$ is FPT($d$) if $p_{\max}$ unary bounded, using the algorithm of Goemans-Rothvoss **[GR]**. Another application: <typo fv:small-caps>Equitable Coloring</typo> is FPT($nd(G)$). | |
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| | * **[PA]** is the book [[https://www.mimuw.edu.pl/~malcin/book/parameterized-algorithms.pdf| Parameterized Algorithms]]. |
| | * **[ND]** [[https://www.lamsade.dauphine.fr/~mlampis/papers/metatheorems_journal.pdf|Algorithmic Meta-theorems for Restrictions of Treewidth]]: a paper which introduced $nd(G)$ and describes the coloring algorithm |
| | * **[NdCol]** [[https://rdcu.be/cUrsc|A note on coloring...]]: a paper by Martin which retells the coloring algorithm by Lampis and points out that it can be solved more efficiently |
| | * **[5M]** [[https://www.sciencedirect.com/science/article/pii/S157252862030030X?ref=pdf_download&fr=RR-2&rr=8317fd563de2b333|Integer programming in parameterized complexity: Five miniatures]] a comprehensive paper about various parameterized integer programming algorithms and their applications to problems on bounded-$nd$ graphs. |
| | * **[GR]** [[https://dl.acm.org/doi/10.1145/3421750|Polynomiality for Bin Packing with a Constant Number of Item Types]] |
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