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Fixed-Parameter Algorithms for Cochromatic Number and Disjoint Rectangle Stabbing [chapter]

Pinar Heggernes, Dieter Kratsch, Daniel Lokshtanov, Venkatesh Raman, Saket Saurabh
2010 Lecture Notes in Computer Science  
We further demonstrate the power of this combination by giving a 2 O(k 2 log k) n log n time algorithm for deciding whether a given set of n non-overlapping axis-parallel rectangles can be stabbed by at  ...  Thus we resolve affirmatively the open question of whether the problem is fixed parameter tractable.  ...  We give a fixed parameter tractable algorithm for Cochromatic Number on perfect graphs in Section 4 and for Disjoint Rectangle Stabbing in Section 5.  ... 
doi:10.1007/978-3-642-13731-0_32 fatcat:mstvuiwhhjgkfmnfegcx35lmmi

Fixed-parameter algorithms for Cochromatic Number and Disjoint Rectangle Stabbing via iterative localization

Pinar Heggernes, Dieter Kratsch, Daniel Lokshtanov, Venkatesh Raman, Saket Saurabh
2013 Information and Computation  
stabbed by at most k of a given set of horizontal and vertical lines. √ n) for partitioning π into the minimum number of monotone subsequences [3].  ...  A natural question which has been left open, and most recently stated at a 2008 Dagstuhl Seminar [18], is whether the problem is fixed parameter tractable (FPT) when parameterized by the number of monotone  ...  The fixed parameter tractable algorithm for Cochromatic Number on perfect graphs is given in Section 4 and for Disjoint Rectangle Stabbing in Section 5. We conclude with some remarks in Section 6.  ... 
doi:10.1016/j.ic.2013.08.007 fatcat:toybexwo6ranvlcvskka7aidju

Solving Partition Problems Almost Always Requires Pushing Many Vertices Around

Iyad Kanj, Christian Komusiewicz, Manuel Sorge, Erik Jan van Leeuwen
2020 SIAM Journal on Discrete Mathematics  
A powerful algorithmic technique that can be used to obtain fixed-parameter algorithms for many cases of (Π A , Π B )-Recognition, as well as several other problems, is the pushing process.  ...  In this paper, we study whether (Π A , Π B )-Recognition problems for which the pushing process yields fixed-parameter algorithms also admit polynomial problem kernels.  ...  [19] to show the fixed-parameter tractability of computing the cochromatic number of perfect graphs and the stabbing number of disjoint rectangles with axes-parallel lines (using the standard parameters  ... 
doi:10.1137/19m1239362 fatcat:s275d4z3dnajzhkmzio3kol4o4

Parameterized Algorithms for Recognizing Monopolar and 2-Subcolorable Graphs [article]

Iyad Kanj, Christian Komusiewicz, Manuel Sorge, Erik Jan van Leeuwen
2018 arXiv   pre-print
In particular, we give fixed-parameter algorithms for two NP-hard (Π_A,Π_B)-Recognition problems, Monopolar Recognition and 2-Subcoloring.  ...  We complement our algorithmic results with several hardness results for (Π_A,Π_B)-Recognition.  ...  [17] introduced iterative localization and used it to develop fixed-parameter tractable algorithms for computing the cochromatic number 1 of permutation graphs, and the stabbing number of disjoint rectangles  ... 
arXiv:1702.04322v2 fatcat:iv2zl54wrzadfa7dx3d4rpcuuq

Cumulative index volumes 1–92

2000 Discrete Applied Mathematics  
Wenger, Ordered stabbing of pairwise disjoint convex sets in linear time 31 (1991) 133-140 Ehrenfeucht, A., G. Rozenberg and R.  ...  Suzuki and 8. Tardos, Algorithms for routing around a rectangle 40 (, J.B.G. and A.H.G. Rinnooy Kan, The rate of convergence to optimality of the LPT rule 14 (1986, G.H., ST. Hedetniemi and D.P.  ... 
doi:10.1016/s0166-218x(00)00210-9 fatcat:vvomn3k7hbbmliptwaczxk6wi4

Solving Partition Problems Almost Always Requires Pushing Many Vertices Around [article]

Iyad Kanj, Christian Komusiewicz, Manuel Sorge, Erik Jan van Leeuwen
2018 pre-print
A powerful algorithmic technique that can be used to obtain fixed-parameter algorithms for many cases of (P_A,P_B)-RECOGNITION, as well as several other problems, is the pushing process.  ...  In this paper, we study whether (P_A,P_B)-RECOGNITION problems for which the pushing process yields fixed-parameter algorithms also admit polynomial problem kernels.  ...  [21] to show the fixed-parameter tractability of computing the cochromatic number of perfect graphs and the stabbing number of disjoint rectangles with axes-parallel lines (using the standard parameters  ... 
doi:10.4230/lipics.esa.2018.51 arXiv:1808.08772v1 fatcat:4u7j5dnrsnecpdeil3s5j7vyum