# Mittagsseminar (in cooperation with M. Ghaffari, A. Steger and B. Sudakov)

__Mittagsseminar Talk Information__ | |

**Date and Time**: Thursday, October 29, 2009, 12:15 pm

**Duration**: This information is not available in the database

**Location**: CAB G51

**Speaker**: Thomas Liphardt

## Finding a Heaviest Triangle is not Harder than Matrix Multiplication (student talk, 45 min.)

The main result of this paper is that finding a heaviest triangle in a vertex-weighted graph on n vertices can be done in the same asymptotic time as finding any triangle. The best algorithm currently known for the latter problem needs time O(n2.376), which is the time needed by the best known algorithm for multiplying two n x n - matrices. The proof of this result is surprisingly elementary, even more so considering that no subcubic algorithm for this problem was known until STOC 2006.

Paper by Artur Czumaj and Andrzej Lingas: Finding a Heaviest Triangle is not Harder than Matrix Multiplication, Proc. of the 18th Symposium on Discrete Algorithms (SODA) 2007.

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