
A polynomialtime algorithm to determine (almost) Hamiltonicity of dense regular graphs
We give a polynomialtime algorithm for detecting very long cycles in de...
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Regular Separability and Intersection Emptiness are Independent Problems
The problem of regular separability asks, given two languages K and L, w...
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Computational Complexity of Synchronization under Sparse Regular Constraints
The constrained synchronization problem (CSP) asks for a synchronizing w...
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Towards Efficient Normalizers of Primitive Groups
We present the ideas behind an algorithm to compute normalizers of primi...
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Continuous Regular Functions
Following Chaudhuri, Sankaranarayanan, and Vardi, we say that a function...
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Regular matroids have polynomial extension complexity
We prove that the extension complexity of the independence polytope of e...
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On the Efficiency of Strategies for Subdividing Polynomial Triangular Surface Patches
In this paper, we investigate the efficiency of various strategies for s...
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Efficient Folding Algorithms for Regular Polyhedra
We investigate the folding problem that asks if a polygon P can be folded to a polyhedron Q for given P and Q. Recently, an efficient algorithm for this problem has been developed when Q is a box. We extend this idea to regular polyhedra, also known as Platonic solids. The basic idea of our algorithms is common, which is called stamping. However, the computational complexities of them are different depending on their geometric properties. We developed four algorithms for the problem as follows. (1) An algorithm for a regular tetrahedron, which can be extended to a tetramonohedron. (2) An algorithm for a regular hexahedron (or a cube), which is much efficient than the previously known one. (3) An algorithm for a general deltahedron, which contains the cases that Q is a regular octahedron or a regular icosahedron. (4) An algorithm for a regular dodecahedron. Combining these algorithms, we can conclude that the folding problem can be solved pseudopolynomial time when Q is a regular polyhedron and other related solid.
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