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Discrete Applied Mathematics
Partitions of graphs into one or two independent sets and cliques
Discrete Mathematics
Graph classes: a survey
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Information Processing Letters
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Journal of Algorithms
Algorithmic Graph Theory and Perfect Graphs (Annals of Discrete Mathematics, Vol 57)
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Combinatorica
Parameterized Complexity Theory (Texts in Theoretical Computer Science. An EATCS Series)
Parameterized Complexity Theory (Texts in Theoretical Computer Science. An EATCS Series)
Approximation Algorithms for Rectangle Stabbing and Interval Stabbing Problems
SIAM Journal on Discrete Mathematics
Constant Approximation Algorithms for Rectangle Stabbing and Related Problems
Theory of Computing Systems
A fixed-parameter algorithm for the directed feedback vertex set problem
Journal of the ACM (JACM)
The Parameterized Complexity of the Rectangle Stabbing Problem and Its Variants
FAW '08 Proceedings of the 2nd annual international workshop on Frontiers in Algorithmics
Improved algorithms for feedback vertex set problems
Journal of Computer and System Sciences
Parameterized Complexity of Stabbing Rectangles and Squares in the Plane
WALCOM '09 Proceedings of the 3rd International Workshop on Algorithms and Computation
Fixed-Parameter algorithms for cochromatic number and disjoint rectangle stabbing
SWAT'10 Proceedings of the 12th Scandinavian conference on Algorithm Theory
Finding odd cycle transversals
Operations Research Letters
Parameterized Complexity
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Given a permutation @p of {1,...,n} and a positive integer k, can @p be partitioned into at most k subsequences, each of which is either increasing or decreasing? We give an algorithm with running time 2^O^(^k^^^2^l^o^g^k^)n^O^(^1^) that solves this problem, thereby showing that it is fixed parameter tractable. This NP-complete problem is equivalent to deciding whether the cochromatic number of a given permutation graph on n vertices is at most k. Our algorithm solves in fact a more general problem: within the mentioned running time, it decides whether the cochromatic number of a given perfect graph on n vertices is at most k. To obtain our result we use a combination of two well-known techniques within parameterized algorithms: iterative compression and greedy localization. Consequently we name this combination ''iterative localization''. We further demonstrate the power of this combination by giving an algorithm with running time 2^O^(^k^^^2^l^o^g^k^)nlogn that decides whether a given set of n non-overlapping axis-parallel rectangles can be stabbed by at most k of a given set of horizontal and vertical lines.