Edward Flathers

Edward Flathers Statistics 565-01 Lee Project Plan 28 September 2012

Proposal

For my class project, I have chosen to work with the paper, “Different Approaches to Solve the 0/1 Knapsack Problem” by Maya Hristakeva and Dipti Shrestha. In the paper, the authors treat the knapsack problem using a variety of algorithmic approaches: brute force, dynamic programming, memory functions, branch and bound, and a greedy algorithm. The algorithms are introduced and then applied to a number of simulations of the knapsack problem in which different parameters are changed. The results show comparison of computer resources used to execute each algorithm under different parameters. The project will begin with some review of the literature surrounding the knapsack problem and the algorithms under consideration. The knapsack problem, a classical NP- complete problem, is unlikely to have significantly different context since the paper was presented in 2004. Of the algorithmic methods, some are very well-established (brute force, branch and bound, greedy) and some are still very much under development (dynamic programming and memory functions). The state of the art for the latter methods may have changed, especially with respect to implementation in newer languages such as R. Next, I will programmatically replicate the methods from the paper. The paper provides pseudocode for implementation of the various algorithms, but does not provide implementation in any specific language. Though the goal of this class project will be to implement algorithms in R, some of the methods may not be approachable in that language and may require other languages to realize. Depending on my access to tools for those languages, I may not be able to implement one or more of the methods. Finally, I will analyze some real data using several of the methods presented in the paper. I have no particular real dataset in mind, but knapsack problems are extremely common in the world, and I expect that I will have ample opportunity to choose an application as the semester continues. As the authors note, since the knapsack problem is NP-complete, exact answers are not possible to compute for realistically large data, so the results will be of the form of estimated solutions and descriptions of the efficiency of the algorithms run.

Work Referenced

Hristakeva, Maya and Dipti Shrestha. “Different Approaches to Solve the 0/1 Knapsack Problem.” Simpson College.

Prof Remark: You need to include a Monte Carlo and a MCMC approach to compare with these different approaches mentioned in this paper.