Constraints on the Extremely-high Energy Cosmic Neutrino Flux with the IceCube 2008-2009 Data

We report on a search for extremely-high energy neutrinos with energies greater than ${10}^6$ GeV using the data taken with the IceCube detector at the South Pole. The data was collected between April 2008 and May 2009 with the half completed IceCube array. The absence of signal candidate events in the sample of 333.5 days of livetime significantly improves model independent limit from previous searches and allows to place a limit on the diffuse flux of cosmic neutrinos with an $E^{-2}$ spectrum in the energy range $2.0 \times 10^{6}$ $-$ $6.3\times {10}^9$ GeV to a level of $E^2 \phi \leq 3.6 \times 10^{-8}$ $\mathrm{G}\mathrm{e}\mathrm{V}\mathrm{c}{\mathrm{m}}^{-2}\mathrm{s}\mathrm{e}{\mathrm{c}}^{-1}\mathrm{s}{\mathrm{r}}^{-1}$.