Mohammad Moharrami's homepage

Welcome to my homepage!
I am an undergraduate student at the Department of Computer Engineering of Sharif University of Technology, Tehran, Iran.
my picture
Contact information:
14, Sa'di, ValiAsr,
Tajrish, Tehran, Iran
Phone: +98 (21) 2273 2969
E-mail:
my last name at CE dot sharif dot edu
Here, you can find my resume, test scores, and transcript.

Research Interests

Research Papers

Lower Bound for Distortion of Planar Graph Embedding in the Plane, with MohammadTaghi Hajiaghayi, Erik Demaine and Mohammad Hossein Bateni
To Appear SoCG 2006, 22nd Annual ACM Symposium on Computational Geometry.

Embedding metrics into constant-dimensional geometric spaces, such as the Euclidean plane, is relatively poorly understood. Motivated by applications in visualization, ad-hoc networks, and molecular reconstruction, we consider the natural problem of embedding shortest-path metrics of unweighted planar graphs (\emph{planar graph metrics}) into the Euclidean plane. It is known that, in the special case of shortest-path metrics of trees, embedding into the plane requires $\Theta(\sqrt n)$ distortion in the worst case \cite{Matousek-trees,BMMV03}, and surprisingly, this worst-case upper bound provides the best known approximation algorithm for minimizing distortion. We answer an open question posed in this work by proving that some planar graph metrics require $\Omega(n^{2/3})$ distortion in any embedding into the plane, proving the first separation between these two types of graph metrics. We also prove that some planar graph metrics require $\Omega(n)$ distortion in any crossing-free straight-line embedding into the plane, suggesting a separation between low-distortion plane embedding and the well-studied notion of crossing-free straight-line planar drawings. Finally, on the upper-bound side, we prove that all outerplanar graph metrics can be embedded into the plane with $O(\sqrt n)$ distortion, generalizing the previous results on trees (both the worst-case bound and the approximation algorithm) and building techniques for handling cycles in plane embeddings of graph metrics.

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