Parameterized complexity theory
Citations
1,544 citations
Cites background from "Parameterized complexity theory"
...The formal foundation for Turing kernelization is the concept of oracle Turing machines (see [189]), where we constrain the power of the oracle to being able to answer only queries that are short in terms of the parameter....
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...The book of Flum and Grohe [189] is an extensive introduction to the area with a strong emphasis on the complexity viewpoint....
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...The area has been developing at such a fast rate that even the two books that appeared in 2006, by Flum and Grohe [189] and Niedermeier [376], do not contain some of the new tools and techniques that we feel need to be taught in a modern introductory course....
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...The book of Flum and Grohe [189] focuses to a large extent on complexity aspects of parameterized algorithmics from the viewpoint of logic, while the material we wanted to cover in the school is primarily algorithmic, viewing complexity as a tool for proving that certain kinds of algorithms do not exist....
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...Our kernelization for d-Hitting Set follows the lines of [189]....
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947 citations
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671 citations
Cites background from "Parameterized complexity theory"
...For more background on parameterized complexity, the reader is referred to [7,24,32]....
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...It is known that FPT = M[1] iff n variable 3-SAT can be solved in 2o(n) time [13,23,32], and FPT = W[1] iff k-Step NonDeterministic Turing Machine Halting is fixed-parameter tractable [22,24,29]....
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642 citations