Years and Authors of Summarized Original Work
2009; Alon, Lokshtanov, Saurabh
2013; Fomin, Villanger
2014; Drange, Fomin, Pilipczuk, Villanger
Problem Definition
A parameterized problem is a language \(L \subseteq \varSigma ^{{\ast}}\times \mathbb{N}\), where \(\varSigma\) is a fixed, finite alphabet. The second component is called the parameter of the problem. The central notion in parameterized complexity is the notion of fixed-parameter tractability (FPT). A parameterized problem L is called FPT if it can be determined in time f(k) ⋅ nc whether or not (x, k) ∈ L, where \(n =\vert (x,k)\vert\), f is a computable function depending only on k, and c is a constant independent of n and k. The complexity class containing all fixed-parameter tractable problems is called FPT.
While in the definition of class FPT, we are happy with any computable function f, from application perspective it is often desirable to have the asymptotic growth of fas slow as possible. Take as an example an FPT...
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Alon N, Lokshtanov D, Saurabh S (2009) Fast FAST. In: Proceedings of the 36th international colloquium of automata, languages and programming (ICALP). Lecture notes in computer science, vol 5555. Springer, Berlin/New York, pp 49–58
Bliznets I, Fomin FV, Pilipczuk M, Pilipczuk M (2014) A subexponential parameterized algorithm for proper interval completion. In: Proceedings of the 22nd annual European symposium on algorithms (ESA 2014). Lecture notes in computer science, vol 8737. Springer, Heidelberg, pp 173–183
Bliznets I, Fomin FV, Pilipczuk M, Pilipczuk M (2014) A subexponential parameterized algorithm for interval completion. CoRR. abs/1402.3473
Drange PG, Fomin FV, Pilipczuk M, Villanger Y (2014) Exploring subexponential parameterized complexity of completion problems. In: Proceedings of the 31st international symposium on theoretical aspects of computer science (STACS). Leibniz international proceedings in informatics (LIPIcs), vol 25. Schloss Dagstuhl – Leibniz-Zentrum fuer Informatik, Dagstuhl, pp 288–299
Fomin FV, Kratsch S, Pilipczuk M, Pilipczuk M, Villanger Y (2013) Tight bounds for parameterized complexity of cluster editing. In: Proceedings of the 30th international symposium on theoretical aspects of computer science (STACS). Leibniz international proceedings in informatics (LIPIcs), vol 20. Schloss Dagstuhl – Leibniz-Zentrum fuer Informatik, Dagstuhl, pp 32–43
Fomin FV, Villanger Y (2013) Subexponential parameterized algorithm for minimum fill-in. SIAM J Comput 42(6):2197–2216
Ghosh E, Kolay S, Kumar M, Misra P, Panolan F, Rai A, Ramanujan MS (2012) Faster parameterized algorithms for deletion to split graphs. In: Proceedings of the 13th Scandinavian symposium and workshops on algorithm theory (SWAT). Lecture notes in computer science, vol 7357. Springer, Berlin/New York, pp 107–118
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Fomin, F.V. (2016). Subexponential Parameterized Algorithms. In: Kao, MY. (eds) Encyclopedia of Algorithms. Springer, New York, NY. https://doi.org/10.1007/978-1-4939-2864-4_780
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