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2ima00 [2016/05/26 11:42]
bmpjansen [Student lectures]
2ima00 [2016/05/26 12:15]
bmpjansen [Student lectures]
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 **Kernels: Chris & Leo.** **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| [[http://​dx.doi.org/​10.1007/​s00224-009-9234-2|
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 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)]]
  
-This uses an approximation ​algorithm, ​which was developed independently by 2 sets of authors. Pick the one you find the easiest to read:+Instead of requiring ​an algorithm ​to find maximum matchingsit 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: Option 1:
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 **Treewidth:​ Henk & Xi.** **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]]
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 +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)
  
2ima00.txt ยท Last modified: 2016/05/26 12:27 by bmpjansen