How to eat 4/9 of a pizza

@article{Knauer2011HowTE,
  title={How to eat 4/9 of a pizza},
  author={K. Knauer and Piotr Micek and T. Ueckerdt},
  journal={Discret. Math.},
  year={2011},
  volume={311},
  pages={1635-1645}
}
Two players want to eat a sliced pizza by alternately picking its pieces. The pieces may be of various sizes. After the first piece is eaten every subsequently picked piece must be adjacent to some previously eaten. We provide a strategy for the starting player to eat 49 of the total size of the pizza. This is best possible and settles a conjecture of Peter Winkler. 
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