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A general method to speed up fixed-parameter-tractable algorithms. (English) Zbl 1014.68064
Summary: A fixed-parameter-tractable algorithm, or FPT algorithm for short, gets an instance $$(I,k)$$ as its input and has to decide whether $$(I,k)\in L$$ for some parameterized problem $$L$$. Many parameterized algorithms work in two stages: reduction to a problem kernel and bounded search tree. Their time complexity is then of the form $$O(p(|I|)+q(k)\xi^k)$$, where $$q(k)$$ is the size of the problem kernel. We show how to modify these algorithms to obtain time complexity $$O(p(|I|)+\xi^k)$$, if $$q(k)$$ is polynomial.

##### MSC:
 68Q25 Analysis of algorithms and problem complexity 68Q15 Complexity classes (hierarchies, relations among complexity classes, etc.)
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##### References:
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