Awake (Skillet album) Awake (Skillet album) Awake is the seventh album by American Christian rock band Skillet. It is the follow-up to their Grammy-nominated album "Comatose". The album was released August 25, 2009 by Lava Records and Ardent Records and debuted at No. 2 on the "Billboard" 200. The album was certified gold by the Recording Industry Association of America (RIAA) on July 27, 2010, and has since gone double platinum, selling over 2,000,000 copies to date. It was nominated for Top Christian Album at the "Billboard" Music Awards 2011 and won. This is the last album to feature guitarist Ben Kasica and
Envy-free item assignment the agents' utilities are not additive, the MNW solution is not necessarily EF1; but if the agents' utilities are at least submodular, the MNW solution satisfies a weaker property called "Marginal-Envy-Freeness except-1-item" (MEF1). There is an alternative criterion called Envy-freeness-except-cheapest (EFx): For each two agents A and B, if we remove from the bundle of B "any" item, then A does not envy B. EFx is strictly stronger than EF1. As of this writing, it is not known whether EFx allocations always exist. Given an allocation "X", define the envy ratio of "i" in "j" as: so the ratio is