Summary of Part 1

This post talks gives a review about the dense linear algebra pattern, the monte carlo and the graph algorithms patterns. The first thing to talk about is the dense linear algebra pattern. The problem of maximizing performance while balancing data movement is an interesting one, and I am sure it is similar to the problems encountered in many different areas of Computer Science. Being a student with research interest in Data Mining, I come across many of these problems frequently. One of the parallels drawn in my research is to minimize the generation of candidate sets to problems (or to completely avoid them), and some of the best algorithms are the ones which are able to utilize the computing power, deliver maximum maximum performance without delivering too much overhead to the system. The question of an algorithm being implementation (or problem-dependent) is also an interesting aspect, and as such many algorithms must be able to generalize over a wider range of datasets. The paper is interesting as it gives an overview of how problems can be modeled as standard equations(or problems) in linear algebra and can solved through the use of libraries.

The second paper talks about the graph algorithms pattern. I can relate to this because I encounter this frequently when solving graph-mining problems. The problem of modeling a data mining problem into a graph-mining problem utilizing graph algorithms is interesting and one of the useful aspects(mentioned in the writeup) is determining theoretical bounds on the performance of different algorithms. For example, one interesting problem which I thought of (on reading the various examples mentioned) is determining dense clusters of friends from a social network graph. I also feel that ignoring the special properties of the graphs(in the context of the problem that we are studying) does not help us develop efficient algorithms (which take advantage of those special properties). The writeup gives a nice overview of recognizing different types of graph structures, (and I think I will refer back to this page when I want to refresh concepts in graph algorithms :)). The last paper is about Monte Carlo patterns. I first came across these patterns as an undergraduate student when I was reading papers in simulated annealing and in particle swarm optimization. I feel that Monte Carlo methods are very useful is solving problems where no known optimal solution exists.