Skillet (band) 2000, Trey McClurkin parted ways with Skillet, and Lori Peters filled the drummer's position. The band released their first worship album, and fourth album overall, "Ardent Worship" in late 2000. The band kept much of their sound from "Invincible" on their next album "Alien Youth". With little time between touring and recording, Skillet released "Alien Youth" on August 28, 2001, which was the first album that John Cooper took on production duties. Before the release of "Alien Youth", Haaland left the band, and Ben Kasica took over on guitar. In 2003, "Collide", the band's sixth studio album, was released by
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