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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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