  A search for extremely high energy cosmic neutrinos has been carried out with
the IceCube Neutrino Observatory. The main signals in the search are
neutrino-induced energetic charged leptons and their rate depends on the
neutrino-nucleon cross section. The upper-limit on the neutrino flux has
implications for possible new physics beyond the standard model such as the
extra space-time dimension scenarios which lead to a cross section much higher
than the standard particle physics prediction. In this study we constrain the
neutrino-nucleon cross section at energies beyond $10^9$ GeV with the IceCube
observation. The constraints are obtained as a function of the extraterrestrial
neutrino flux in the relevant energy range, which accounts for the
astrophysical uncertainty of neutrino production models.
