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 Keyue Gao Mathematics , 2012, Abstract: This paper deals with a problem in which two players share a previously sliced pizza and try to eat as much amount of pizza as they can. It takes time to eat each piece of pizza and both players eat pizza at the same rate. One is allowed to take a next piece only after the person has finished eating the piece on hand. Also, after the first piece is taken, one can only take a piece which is adjacent to already-taken piece. This paper shows that, in this real time setting, the starting player can always eat at least two-fifth of the total size of the pizza. However, this may not be the best possible amount the starting player can eat. It is a modified problem from an original one where two players takes piece alternatively instead.
 Mathematics , 2015, Abstract: We propose a class of two person perfect information games based on weighted graphs. One of these games can be described in terms of a round pizza which is cut radially into pieces of varying size. The two players alternately take pieces subject to the following rule: Once the first piece has been chosen, all subsequent selections must be adjacent to the hole left by the previously taken pieces. Each player tries to get as much pizza as possible. The original pizza problem was to settle the conjecture that Player One can always get at least half of the pizza. The conjecture turned out to be false. Our main result is a complete solution of a somewhat simpler class of games, concatenations of stacks and two-ended stacks, and we provide a linear time algorithm for this. The algorithm and its output can be described without reference to games. It produces a certain kind of partition of a given finite sequence of real numbers. The conditions on the partition involve alternating sums of various segments of the given sequence. We do not know whether these partitions have applications outside of game theory. The algorithm leads to a quadratic time algorithm which gives the value and an optimal initial move for pizza games. We also provide some general theory concerning the semigroup of equivalence classes of graph games.
 Mathematics , 2005, Abstract: Consider n straight line cuts of a circular pizza made so as to maximize the number of pieces. We investigate how fair such a maximal division may be and how many slices are obtained if the cuts are successfully made with a certain probability.