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2ima00 [2016/05/12 12:17]
bmpjansen [Student lectures]
2ima00 [2016/05/26 12:18]
bmpjansen [Student lectures]
Line 121: Line 121:
 === Programming pairs for implementation === === 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: +**Kernels: Chris & Leo.**
-Chris & Leo.+
-Treewidth:​ +The following paper gives a kernel that is not as small, but is easier to compute, than the one given in the bookIn particular, read Section 4 of this paper:
-Henk & Xi.+
-Parameterized by solution size (iterative compression & randomized):​ +[[http://​​10.1007/​s00224-009-9234-2| 
-Huib & Stefan.+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://​​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://​​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://​​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://​​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.** 
 +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://​​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