====== Introduction to Parameterized Algorithms 23/24 ======


===== Tutorial sessions =====

Tutorials are led by [[https://kam.mff.cuni.cz/~tung|Tung]].
[[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.


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^ 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($nd(G)$). |

  * **[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]]