The allocation problem with submodular utility functions ( preliminary version )

@inproceedings{Feige2006TheAP,
  title={The allocation problem with submodular utility functions ( preliminary version )},
  author={Uriel Feige and Jan Vondr{\'a}k},
  year={2006}
}
We consider the problem of maximizing welfare when allocating items to players with submodular utility functions. Our main result is a way of rounding any fractional solution to a linear programming relaxation to this problem so as to give a feasible solution of welfare at least 1−1/e+2 of the value of the fractional solution, where 2 > 0 is some fixed constant. This resolves the question of whether the previous approximation ratio of 1 − 1/e (for which there now are three different proofs, one… CONTINUE READING

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