On the complexity of the pancake problem

• Autores: Fuxiang Yu
• Localización: Mathematical Logic Quarterly, ISSN 0942-5616, Vol. 53, Nº. 4-5, 2007, págs. 532-546
• Idioma: inglés
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• Resumen

  • We study the computational complexity of finding a line that bisects simultaneously two sets in the two-dimensional plane, called the pancake problem, using the oracle Turing machine model of Ko. We also study the basic problem of bisecting a set at a given direction. Our main results are:

    (1) The complexity of bisecting a nice (thick) polynomial-time approximable set at a given direction can be characterized by the counting class #P.

    (2) The complexity of bisecting simultaneously two linearly separable nice (thick) polynomial-time approximable sets can be characterized by the counting class #P.

    (3) For either of these two problems, without the thickness condition and the linear separability condition (for the two-set case), it is arbitrarily hard to compute the bisector, even if it is unique.