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2ima00 [2016/05/26 11:38]
bmpjansen [Student lectures]
2ima00 [2016/05/26 12:15]
bmpjansen [Student lectures]
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 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. 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. + 
-[[http://​dx.doi.org/​10.1007/​s00224-009-9234-2"|+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: 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)]] A Cubic Kernel for Feedback Vertex Set and Loop Cutset. Theory Comput. Syst. 46(3): 566-597 (2010)]]
  
-Treewidth+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
-Henk & Xi.+ 
 +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]] [[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) [[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)
  
-Parameterized by solution size (iterative compression & randomized):​ +**Parameterized by solution size (iterative compression & randomized):​ Huib & Stefan.**
-Huib & Stefan.+
  
 [[http://​dx.doi.org/​10.1016/​j.ipl.2014.05.001|Tomasz Kociumaka, Marcin Pilipczuk: [[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)]] Faster deterministic Feedback Vertex Set. Inf. Process. Lett. 114(10): 556-560 (2014)]]
2ima00.txt · Last modified: 2016/05/26 12:27 by bmpjansen