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Parameterized Computation and Complexity: A New Approach Dealing with NP-Hardness

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Abstract

The theory of parameterized computation and complexity is a recently developed subarea in theoretical computer science. The theory is aimed at practically solving a large number of computational problems that are theoretically intractable. The theory is based on the observation that many intractable computational problems in practice are associated with a parameter that varies within a small or moderate range. Therefore, by taking the advantages of the small parameters, many theoretically intractable problems can be solved effectively and practically. On the other hand, the theory of parameterized computation and complexity has also offered powerful techniques that enable us to derive strong computational lower bounds for many computational problems, thus explaining why certain theoretically tractable problems cannot be solved effectively and practically. The theory of parameterized computation and complexity has found wide applications in areas such as database systems, programming languages, networks, VLSI design, parallel and distributed computing, computational biology, and robotics.

This survey gives an overview on the fundamentals, algorithms, techniques, and applications developed in the research of parameterized computation and complexity. We will also report the most recent advances and excitements, and discuss further research directions in the area.

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Author information

Correspondence to Jian-Er Chen.

Additional information

This research is supported in part by the National Natural Science Foundation of China under Grants No.60373083 and No.60433020, and by the Changjiang Scholar Reward Project of Ministry of Education, P.R. China.

Jian-Er Chen got his B.S. degree in computer science in 1982 from Central South University, China, and his Ph.D. degree in computer science in 1987 from Courant Institute, New York University, USA, where he was awarded the Janet Fabri Award for the best Ph.D. dissertation. After graduation from NYU, he went to the Department of Mathematics at Columbia University, USA, where he received the Ph.D. degree in mathematics in 1990. Since then, he has been with the Department of Computer Science at Texas A&M University, USA, where he is a professor. Currently, he is a ChangJiang Scholar Professor at Central South University, China. His research interests include theoretical computer science, bioinformatics, computer networks, and computer graphics. He has published over 120 journal and conference papers in these areas, and received numerous awards, including the Research Initiation Award in 1991 from US National Science Foundation, TEES Select Young Faculty Award in 1993 and Distinguished Faculty Achievement Award in 1998 from Texas A&M University, Oversea Distinguished Young Scholars Award in 2000 from the National Natural Science Foundation of China, and Natural Science Award (first class) in 2003 from MOE, China.

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Chen, J. Parameterized Computation and Complexity: A New Approach Dealing with NP-Hardness. J Comput Sci Technol 20, 18–37 (2005). https://doi.org/10.1007/s11390-005-0003-7

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Keywords

  • algorithm
  • computational
  • complexity
  • NP-completeness
  • parameterized computation
  • approximation algorithm