Computing a ham-sandwich cut in two dimensions
Journal of Symbolic Computation
Bisections and ham-sandwich cuts of convex polygons and polyhedra
Information Processing Letters
Complexity theory of real functions
Complexity theory of real functions
STOC '92 Proceedings of the twenty-fourth annual ACM symposium on Theory of computing
The power of the middle bit of a #P function
Journal of Computer and System Sciences
Computational Complexity of Two-Dimensional Regions
SIAM Journal on Computing
On closure properties of #P in the context of PF&j0;#P
Journal of Computer and System Sciences
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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; and (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).