2ima00

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2ima00 [2016/04/28 14:56] bmpjansen [Schedule] |
2ima00 [2016/05/26 12:16] bmpjansen [Student lectures] |
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==== Prequisites ==== | ==== Prequisites ==== | ||

- | You can take this course if you have completed at least one of the courses Advanced Algorithms (2IL45), Geometric Algorithms (2IL55), Algorithms for massive data (2IL75) or Algorithms for geographic data (2IL76) successfully. However, if your study plan allows it, it is better to complete at least two of these courses before taking 2IL95. | + | You can take this course if you have completed at least one of the courses Advanced Algorithms (2IL45), Geometric Algorithms (2IL55), Algorithms for massive data (2IL75) or Algorithms for geographic data (2IL76) successfully. However, if your study plan allows it, it is better to complete at least two of these courses before taking 2IMA00. |

If you have not completed any of the aforementioned courses, but you have completed other Master's courses that are highly relevant to the topic of the seminar, then please contact the [[#instructors]] to discuss if you can be admitted to the course. | If you have not completed any of the aforementioned courses, but you have completed other Master's courses that are highly relevant to the topic of the seminar, then please contact the [[#instructors]] to discuss if you can be admitted to the course. | ||

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| 8 | Using linear programming in parameterized algorithms | Cygan et al. 2.5 & 3.4 | ? | | | 8 | Using linear programming in parameterized algorithms | Cygan et al. 2.5 & 3.4 | ? | | ||

| 9 | Important separators | Cygan et al. 8.1-8.3 | ? | | | 9 | Important separators | Cygan et al. 8.1-8.3 | ? | | ||

+ | |||

+ | === Programming pairs for implementation === | ||

+ | The literature linked to below can be accessed when logged into the TU/e network, either through VPN or by physically being present at TU/e. | ||

+ | |||

+ | **Kernels: Chris & Leo.** | ||

+ | |||

+ | The following paper gives a kernel that is not as small, but is easier to compute, than the one given in the book. In particular, read Section 4 of this paper: | ||

+ | |||

+ | [[http://dx.doi.org/10.1007/s00224-009-9234-2| | ||

+ | Hans L. Bodlaender, Thomas C. van Dijk: | ||

+ | A Cubic Kernel for Feedback Vertex Set and Loop Cutset. Theory Comput. Syst. 46(3): 566-597 (2010)]] | ||

+ | |||

+ | Instead of requiring an algorithm to find maximum matchings, it just needs an approximation algorithm for (weighted) feedback vertex set. It was developed independently by 2 sets of authors. Pick the one you find the easiest to read: | ||

+ | |||

+ | Option 1: | ||

+ | |||

+ | [[http://dx.doi.org/10.1137/S0895480196305124|Vineet Bafna, Piotr Berman, Toshihiro Fujito: | ||

+ | A 2-Approximation Algorithm for the Undirected Feedback Vertex Set Problem. SIAM J. Discrete Math. 12(3): 289-297 (1999)]] | ||

+ | |||

+ | Option 2: | ||

+ | |||

+ | [[https://dx.doi.org/10.1016%2F0004-3702%2895%2900004-6|Becker, Ann; Geiger, Dan (1996), "Optimization of Pearl's method of conditioning and greedy-like approximation algorithms for the vertex feedback set problem.", Artificial Intelligence 83 (1): 167–188]] | ||

+ | |||

+ | **Treewidth: Henk & Xi.** | ||

+ | |||

+ | There are 2 approaches for solving the problem when you have a tree decomposition. The first one has a running time of 3^k * poly(n), harder to understand, but may be easier to implement: | ||

+ | |||

+ | [[https://arxiv.org/pdf/1103.0534v1.pdf|Cygan et al.: Solving connectivity problems parameterized by treewidth in single exponential time]] | ||

+ | |||

+ | The next approach has a worse factor f(k), but a better polynomial term (linear), and is conceptually simpler: | ||

+ | |||

+ | [[http://link.springer.com/chapter/10.1007%2F3-540-36379-3_25|Ton Kloks, C.M. Lee, Jiping Liu. New Algorithms for k-Face Cover, k-Feedback Vertex Set, and k-Disjoint Cycles on Plane and Planar Graphs]] (page 8 and further) | ||

+ | |||

+ | I don't know which of the 2 approaches will be faster on the inputs we have; one has a worse polynomial term, the other has a worse factor f(k). I don't think it is feasible to implement both, given the time. Pick one of the two and go for it. | ||

+ | |||

+ | **Parameterized by solution size (iterative compression & randomized): Huib & Stefan.** | ||

+ | |||

+ | [[http://dx.doi.org/10.1016/j.ipl.2014.05.001|Tomasz Kociumaka, Marcin Pilipczuk: | ||

+ | Faster deterministic Feedback Vertex Set. Inf. Process. Lett. 114(10): 556-560 (2014)]] |

2ima00.txt · Last modified: 2016/05/26 12:27 by bmpjansen