Lecture 20 : Splitting Algorithms

Randomized Algorithm For 3-Set Splitting Problem and it's Markovian Model

In this paper we restrict every set splitting problem to the special case in which every set has just three elements. This restricted version is also NP-complete. Then, we introduce a general conversion from any set splitting problem to 3-set splitting. Then we introduce a randomize algorithm, and we use Markov chain model for run time complexity analysis of this algorithm. In the last section ...

Numerical Solution of Reservoir Flow Models Based Onlarge Time Step Operator Splitting

During recent years the authors and collaborators have been involved in an activity related to the construction and analysis of large time step operator splitting algorithms for the numerical simulation of multi-phase ow in heterogeneous porous media. The purpose of these lecture notes is to review some of this activity. We illustrate the main ideas behind these novel operator splitting algorit...

First order algorithms in variational image processing

The success of non-smooth variational models in image processing is heavily based on efficient algorithms. Taking into account the specific structure of the models as sum of different convex terms, splitting algorithms are an appropriate choice. Their strength consists in the splitting of the original problem into a sequence of smaller proximal problems which are easy and fast to compute. Opera...

CS 229 r : Algorithms for Big Data Fall 2013 Lecture 20 — November 7 , 2013

Advanced Algorithms December 23 , 2004 Lecture 20 : LT Codes Lecturer : Amin

Random linear fountain codes were introduced in the last lecture as a sparse-graph codes for channels with erasure. It turned out that their encoding and decoding costs were quadratic and cubic in the number of packets encoded. We study Luby Transform (LT) codes in this lecture, pioneered by Michael Luby, that retains the good performance of random linear fountain code, while drastically reduci...