Titlebook: Parameterized Complexity; R. G. Downey,M. R. Fellows Book 1999 Springer Science+Business Media New York 1999 Algorithms.Automat.Graph.algo

小口啜饮

The Basic Class ,[1] and an Analog of Cook’s Theoremt and natural NP-complete problems. If . of them were solvable in polynomial-time, then . of them would be. Moreover, other than a few exceptions, if a natural problem is in . and is apparently not in ., then the problem seems to always be .-complete.

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The Basic Definitions parameterized language ., we call . the parameter. Usually the parameter will be a positive integer, but it might be a graph or algebraic structure. However, in the interest of readability and with no loss of generality, we will usually identify the domain of the parameter as the natural numbers N

新手

Optimization Problems, Approximation Schemes, and Their Relation with tour) rather than solve a related decision problem. Furthermore, even if we demonstrate that some problem has no fast solution, it is often acceptable to find an approximate solution to some desired performance ratio. In this section, we will see that parametric complexity and approximatibility are

conscience

Miscellaneous Techniquestreewidth ideas of Chapter 6. The first is the basic graph-theoretic algorithmic technique of depth-first search. The second involves a clever utilization of tree decompositions in attacking subgraph problems. The third technique employs a family of number-theoretic hash functions to address paramet

ICLE

极端的正确性

The Basic Class ,[1] and an Analog of Cook’s Theoremtification of classes of intractable problems. In the case of .-completeness, recall that a language . is a member of the class . iff there is a polynomial-time relation . and a polynomial . such that. ∈ . iff ∃.[|.| ≤ .(|.|) ∧ .(., .) holds]For instance, if . is the collection of satisfiable formul

脱水

Mendacious

observatory

Beyond ,[,]-Hardnessppens if we have no bound on the depth and simply look at parameterized problems of “polynomial size.” When we do this, we arrive at classes hard for U..[.]. The study of such classes is the theme of the present chapter. Two important classes immediately suggest themselves. These are the classes .[.

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Fixed Parameter Analogs of , and ,-Move Gamesproblems are considered. So too, the same situation seems to occur when we look at parameterized .. Of course, a natural parameterized space class suggests itself if we wish to consider fixed-parameter space complexity.