Abstract
Parameterized computation theory has developed rapidly over the last two decades. In theoretical computer science, it has attracted considerable attention for its theoretical value and significant guidance in many practical applications. We give an overview on parameterized algorithms for some fundamental NP-hard problems, including MaxSAT, Maximum Internal Spanning Trees, Maximum Internal Out-Branching, Planar (Connected) Dominating Set, Feedback Vertex Set, Hyperplane Cover, Vertex Cover, Packing and Matching problems. All of these problems have been widely applied in various areas, such as Internet of Things, Wireless Sensor Networks, Artificial Intelligence, Bioinformatics, Big Data, and so on. In this paper, we are focused on the algorithms’ main idea and algorithmic techniques, and omit the details of them.
Highlights
In the modern society, computers play an important role in solving optimization problems, most of which are shown to be computationally hard in theory
There are a great deal of computational problems derived from practical applications which can be modeled as combinatorial optimization problems
Algorithmic techniques of parameterized algorithms In this subsection, we show some algorithmic techniques for fixed-parameter tractable (FPT) algorithms and kernelization
Summary
Computers play an important role in solving optimization problems, most of which are shown to be computationally hard in theory. Many new and powerful techniques have attracted a great attention in computer science, and have been successfully used in solving optimal problems in a body of applications. There are a great deal of computational problems derived from practical applications which can be modeled as combinatorial optimization problems. Some of them turned out to be computationally hard to be solved when the input size of these problems are considerably large. Due to the huge amount of information and data to be processed, the existing computers often fall into an awkward situation of “powerlessness” when solving many practical computing problems. It is unlikely for them to solve these problems in acceptable time
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