2ima00

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2ima00 [2016/04/26 17:02] bmpjansen [Student lectures] |
2ima00 [2016/05/26 12:27] 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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|2| Tue| 26-Apr| 15:45-17:30| MF15| Literature study| | |2| Tue| 26-Apr| 15:45-17:30| MF15| Literature study| | ||

|2| Thu| 28-Apr| 10:45-12:30| MF13| Orientation on implementation challenge| | |2| Thu| 28-Apr| 10:45-12:30| MF13| Orientation on implementation challenge| | ||

- | |3| Tue| 03-May| 15:45-17:30| MF15| Student lecture 1| | + | |3| Tue| 03-May| 15:45-17:30| MF15| Student lecture 1 (Bart)| |

|3| Thu| 05-May| 10:45-12:30| MF13| **No meeting**| | |3| Thu| 05-May| 10:45-12:30| MF13| **No meeting**| | ||

- | |4| Tue| 10-May| 15:45-17:30| MF15| Student lecture 2| | + | |4| Tue| 10-May| 15:45-17:30| MF15| Student lecture 2 (Huib)| |

|4| Thu| 12-May| 10:45-12:30| MF13| Brainstorm| | |4| Thu| 12-May| 10:45-12:30| MF13| Brainstorm| | ||

- | |5| Tue| 17-May| 15:45-17:30| MF15| Student lecture 3| | + | |5| Tue| 17-May| 15:45-17:30| MF15| Student lecture 3 (Henk)| |

- | |5| Thu| 19-May| 10:45-12:30| MF13| Student lecture 4| | + | |5| Thu| 19-May| 10:45-12:30| MF13| Student lecture 4 (Stefan)| |

- | |6| Tue| 24-May| 15:45-17:30| MF15| Student lecture 5| | + | |6| Tue| 24-May| 15:45-17:30| MF15| Student lecture 5 (Leo)| |

|6| Thu| 26-May| 10:45-12:30| MF13| Brainstorm| | |6| Thu| 26-May| 10:45-12:30| MF13| Brainstorm| | ||

|7| Tue| 31-May| 15:45-17:30| MF15| **No meeting**| | |7| Tue| 31-May| 15:45-17:30| MF15| **No meeting**| | ||

|7| Thu| 02-Jun| 10:45-12:30| MF13| **No meeting**| | |7| Thu| 02-Jun| 10:45-12:30| MF13| **No meeting**| | ||

- | |8| Tue| 07-Jun| 15:45-17:30| MF15| Student lecture 6| | + | |8| Tue| 07-Jun| 15:45-17:30| MF15| Student lecture 6 (Xi)| |

- | |8| Thu| 09-Jun| 10:45-12:30| MF13| Student lecture 7| | + | |8| Thu| 09-Jun| 10:45-12:30| MF13| Student lecture 7 (Chris)| |

|9| Tue| 14-Jun| 15:45-17:30| MF15| Student lecture 8| | |9| Tue| 14-Jun| 15:45-17:30| MF15| Student lecture 8| | ||

|9| Thu| 16-Jun| 10:45-12:30| MF13| Student lecture 9| | |9| Thu| 16-Jun| 10:45-12:30| MF13| Student lecture 9| | ||

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^ Lecture number ^ Topic ^ Source material ^ Lecturer ^ | ^ Lecture number ^ Topic ^ Source material ^ Lecturer ^ | ||

- | | 1 | More kernelization algorithms | Cygan et al. Chapter 2, **not** 2.5 | Boshen | | + | | 1 | More kernelization algorithms | Cygan et al. Chapter 2, **not** 2.5 | <del>Boshen</del> Bart | |

| 2 | Iterative compression | Cygan et al. Chapter 4, **not** 4.3.2 | Huib | | | 2 | Iterative compression | Cygan et al. Chapter 4, **not** 4.3.2 | Huib | | ||

| 3 | Treewidth | Cygan et al. 7.1-7.3.1 | Henk | | | 3 | Treewidth | Cygan et al. 7.1-7.3.1 | Henk | | ||

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| 5 | Advanced kernelization algorithms | Cygan et al. Section 9.1 | Leo | | | 5 | Advanced kernelization algorithms | Cygan et al. Section 9.1 | Leo | | ||

| 6 | Improving dynamic programming on tree decompositions | Cygan et al. Chapter 11 | Xi | | | 6 | Improving dynamic programming on tree decompositions | Cygan et al. Chapter 11 | Xi | | ||

- | | 7 | W[1]-hardness | Cygan et al. Chapter 13 | ? | | + | | 7 | W[1]-hardness | Cygan et al. Chapter 13 | Chris | |

| 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. To **find** a tree decomposition, you can use one of the heuristics described in this paper: | ||

+ | |||

+ | [[http://dx.doi.org/10.1016/j.ic.2009.03.008|Hans L. Bodlaender, Arie M. C. A. Koster: | ||

+ | Treewidth computations I. Upper bounds. Inf. Comput. 208(3): 259-275 (2010)]] | ||

+ | |||

+ | Within the framework of iterative compression and you have *some* feedback vertex set X in your graph G, you can also make a tree decomposition by making a tree decomposition for the forest G - X (which is easy) and then adding all vertices of X to all bags. Afterwards, you can try to make it better by removing vertices from X from bags when the tree decomposition remains valid after removing a vertex from a bag. | ||

+ | |||

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

+ | |||

+ | For the iterative compression algorithm, I think the book gives sufficient details to build an implementation from. There is a theoretically faster algorithm, which is linked below. You could read it for inspiration, but it's not necessary and I do not think it is feasible to implement it fully because it needs a subroutine with matroid computations. | ||

+ | |||

+ | [[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)]] | ||

+ | |||

+ | For the randomized algorithm, I don't know of any additional literature. You could search by yourself. |

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