PPT-Parameterised Complexity

Algorithms and Networks 20162017 Johan M M van Rooij Hans L Bodlaender This lecture Classical complexity P vs NP Conditional nonexistence proofs Parameterised complexity. How to celebrate it, leverage it, and NOT avoid it!. Are YOU sufficiently complex?. Simple = Best. FROM OCCAM’S . RAZOR. COMPLEXITY. Are YOU sufficiently complex?. Simple = Best. Simple but no. Simpler. China Theory Week, Aarhus. August 13, 2012. Today’s Goal:. To present new developments in a line of research dating back to 2002, presenting some unexpected connections between. Kolmogorov. Complexity (the theory of randomness), and. and . Hierarchy. Concept of Complexity. “whole is more than the sum of its parts”. Holism. new properties not found in subsystems. “mechanistic explanations of emergence rejected”. Weaker view of emergence. Lecture 1: . Intro; Turing machines; . Class P and NP . . . Indian Institute of Science. About the course. Computational complexity attempts . to classify computational . problems. Lecture 1: . Intro; Turing machines; . Class P and NP . . . Indian Institute of Science. About the course. Computational complexity attempts . to classify computational . problems. . Policy. problems in environment & . sustainability. Steve Dovers. Fenner. School of Environment & . Society. 21 May 2013. Complexity Dovers 2013. 2. Context & coverage. Many definitions of complexity, wicked problems . How Understanding Complexity Promotes Simplicity. Why is writing software hard?. ^. great. http://www.infoq.com/presentations/Simple-Made-Easy. Our duty as software architects is to understand and manage complexity. Theophilus Benson (tbenson@cs.wisc.edu). Aditya Akella (akella@cs.wisc.edu). David A Maltz (dmaltz@microsoft.com). Enterprise Networks. Intricate logical and physical topologies. Diverse network devices. William Marsh, william@dcs.qmul.ac.uk. Risk Assessment and Decision Analysis Research Group. Acknowledgements. Joint work with . George Bearfield. Rail Safety and Standards Board (RSSB), London. Aims. Adaptive management in a volatile and complex world. Dr Jean Boulton. Visiting Senior Research Fellow, DSPS, University of Bath. Visiting Fellow, . Cranfield. School of Management. Director, Claremont Management Consultants Ltd. Toniann. . Pitassi. University of Toronto. 2-Party Communication Complexity. [Yao]. 2-party communication: . each party has a dataset. . Goal . is to compute a function f(D. A. ,D. B. ). m. 1. m. 2. Fall . 2011. Sukumar Ghosh. What is an algorithm. . A finite set (or sequence) of . precise instructions . for performing a computation. . . . Example: Maxima finding. . . procedure . max. (. What is the best way to measure the time complexity of an algorithm?. - Best-case run time?. - Worst-case run time?. - Average run time?. Which should we try to optimize?. Best-Case Measures. How can we modify almost any algorithm to have a good best-case running time?. Lijie. Chen. MIT. Today’s Topic. Background. . What is Fine-Grained Complexity?. The Methodology of Fine-Grained Complexity. Frontier: Fine-Grained Hardness for Approximation Problems. The Connection.