1. Igor Balla REU DIMACS 2010

2. Metric Spaces 1. 2. 3. 4.

3. Graph Metrics

4. Metric Embedding

5. Approximating Cycle Metrics

6. Probabilistic Approximations by Tree Metrics

7. Directions for Further Research 1. Bartal, Y. 1996. Probabilistic approximations of metric spaces and its algorithmic applications. In Proceedings of the 37 th Annual Symposium on Foundations of Computer Science (October 14-16, 1996). FOCS. IEEE Computer Society, Washington, DC, 184 2. Fakcharoenphol, J., Rao, S., Talwar, K. 2004. A tight bound on approximating arbitrary metrics by tree metrics. J. Comput. Syst. Sci. 69, 3 (Nov. 2004), 485-497. 3. Karp, R. 1989. A 2k-competitive algorithm for the circle. Manuscript (August 1989) References