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2010
Springer

Fixed-Parameter Algorithms for Cochromatic Number and Disjoint Rectangle Stabbing

9 years 12 months ago
Fixed-Parameter Algorithms for Cochromatic Number and Disjoint Rectangle Stabbing
Given a permutation π of {1, . . . , n} and a positive integer k, we give an algorithm with running time 2O(k2 log k) nO(1) that decides whether π can be partitioned into at most k increasing or decreasing subsequences. Thus we resolve affirmatively the open question of whether the problem is fixed parameter tractable. This NP-complete problem is equivalent to deciding whether the cochromatic number, partitioning into the minimum number of cliques or independent sets, of a given permutation graph on n vertices is at most k. In fact, we give a more general result: within the mentioned running time, one can decide 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, namely greedy localization and iterative compression. We further demonstrate the power of this combination by giving a 2O(k2 log k) n log n time algorithm for deciding whether a given set ...
Pinar Heggernes, Dieter Kratsch, Daniel Lokshtanov
Added 11 Jul 2010
Updated 11 Jul 2010
Type Conference
Year 2010
Where SWAT
Authors Pinar Heggernes, Dieter Kratsch, Daniel Lokshtanov, Venkatesh Raman, Saket Saurabh
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