Some New Directions and Questions in Parameterized Complexity

Downey, Rodney G.; McCartin, Catherine

doi:10.1007/978-3-540-30550-7_2

Cited by 3 publications

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“…If the reader finds this all useful, then we refer him/her to two recent issues of the The Computer Journal [128] devoted to aspects and applications of parameterized complexity, to the survey of Downey and McCartin [134] on parameterized algorithms, the (somewhat dated) survey Downey [116] for issues in complexity, and other articles such as [126,131,132,[141][142][143] as well as the books by Downey and Fellows [125], Niedermeier [240] and Flum and Grohe [154].…”

Section: Other Coping Strategiesmentioning

confidence: 99%

Confronting intractability via parameters

Downey

Thilikos

2011

Computer Science Review

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One approach to confronting computational hardness is to try to understand the contribution of various parameters to the running time of algorithms and the complexity of computational tasks. Almost no computational tasks in real life are specified by their size alone. It is not hard to imagine that some parameters contribute more intractability than others and it seems reasonable to develop a theory of computational complexity which seeks to exploit this fact. Such a theory should be able to address the needs of practicioners in algorithmics. The last twenty years have seen the development of such a theory. This theory has a large number of successes in terms of a rich collection of algorithmic techniques both practical and theoretical, and a fine-grained intractability theory. Whilst the theory has been widely used in a number of areas of applications including computational biology, linguistics, VLSI design, learning theory and many others, knowledge of the area is highly varied. We hope that this article will show both the basic theory and point at the wide array of techniques available. Naturally the treatment is condensed, and the reader who wants more should go to the texts of Downey and Fellows [125], Flum and Grohe [155], Niedermeier [240], and the upcoming undergraduate text Downey and Fellows [127].

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