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Everything about Parameterized complexity

Branch of computational complexity theory

In computer science, parameterized complexity is a branch of computational complexity theory that focuses on classifying computational problems according to their inherent difficulty with respect to multiple parameters of the input or output. The complexity of a problem is then measured as a function of those parameters. Then the theory analyses how the running time for solutions to the problem behave as the parameters get larger. To illustrate the idea, the for a fixed k we can solve instances of vertex cover problem in linear time, whereas the only known algorithms for dominating set problem is more or less search all possible size k subsets and hence require about Ω(n^k) time. When this idea is made formal, the first behaviour is called fixed parameter tractability, since, although both are polynomial time algorithms, the former is of the form O(n^c) independent of the parameter, and the latter is of the form Ω(n^{f ). Wikipedia →

🧭 Start here: a 6-step reading path

  1. Read the overview: Parameterized complexityA 5-minute orientation
  2. Skim a recent paper: Hyperparameter Search for Machine Learning Algorithms for Optimizing the Computational ComplexityInfluential work since 2022
  3. Pick up a classic book: Cognition and IntractabilityThe most-reprinted book on the subject
  4. Read the landmark paper: AD Model Builder: using automatic differentiation for statistical inference of highly parameterized complex nonlinear modelsCited 1,545 times
  5. Go sideways: Parameterized approximation algorithmA closely related topic
  6. Go sideways: KernelizationA closely related topic

📖 Definitions

No dictionary entry for this exact phrase.

🗂️ The subject at a glance

  1. Setup
  2. Complexity classes
  3. Hierarchies

🏆 Landmark papers (most cited)

🆕 Influential since 2022

📚 Books worth reading

Ranked by number of editions on Open Library, a rough measure of how lasting a book is.

🔗 Related topics