COEN279 - Design and Analysis of Algorithms Probabilistic Analysis and Randomized Algorithm Dr. Tunghwa Wang Fall 2016 09/22/2016 Dr. Tunghwa Wang 1 Announcement Always read the document online unless necessary to download: Files could be updated. For the first week, everything is not well prepared yet: Linux account: Use putty to work remotely. E-mail: Automatic forwarded to
[email protected] In case you receive from this account instead of
[email protected]. Bonus assignments: #2 – deadline is extended to 09/25. Future ones – due on Thursday of the week 09/20/2016 Dr. Tunghwa Wang 2 Probabilistic Analysis It is the use of probability in the analysis of problems and thus the algorithm designed to solve these problems. review We compute the average-case running time by taking the average over all the possible inputs – it is average-case running time. The distribution of the inputs is the key to the analysis: We know the distribution of inputs. We assume the model of distribution function of inputs. Otherwise, we cannot do probabilistic analysis. 09/22/2016 Dr. Tunghwa Wang 3 Randomized Algorithms Tools and techniques widely used in many applications. Benefits: Simplicity Speed Robustness Inputs: generated using random number generator Pseudo random numbers Distribution functions Queueing models More Initial values: Randomized initial values of internal variables do not make the algorithm a randomized algorithm. By the nature, they can also be initialized with any valid values, say all initialized to 0. 09/22/2016 Dr. Tunghwa Wang 4 Probabilistic or Randomized Algorithm At least once during the algorithm, a random number is used to make a decision instead of spending time to work out which alternative is best.