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Jul
3
comment Number of Configurations in the optimal Hanoi tower
"It seems forcing the number of disks on all 3 towers specifies a unique position" _ this seems to imply that $2^n \in O(n^3)$ :)
Jun
25
awarded  Informed
May
2
revised Number of Configurations in the optimal Hanoi tower
added 450 characters in body; edited tags; edited title
May
2
comment Number of Configurations in the optimal Hanoi tower
Well, I see these connections can be arbitrary and there might be no nice way to show the equivalence. I just wanted to have a closed formula for Hanoi tower configurations, from the computational perspective, formulas I see with the equal sequences can be calculated in linear time with respect to $n$, whilst recurrent formula for Hanoi configurations takes cubic time.
Apr
30
awarded  Critic
Apr
30
asked Number of Configurations in the optimal Hanoi tower
Jan
11
awarded  Editor
Jan
11
revised computational complexity
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Jan
9
awarded  Scholar
Jan
9
accepted computational complexity
Jan
8
awarded  Supporter
Jan
8
comment computational complexity
I agree with connected components and retraction of boundary, but after these operations we are still dealing with quite arbitrary structure. We can even make things "easier" and assume that every edge is incident with at most 3 triangles by simple topological transformation. If we consider dual problem, take 1 vertex in each triangle and connect two vertices if their respective triangles share edges, we get: in somewhat special graph we need to find cubic planar 3-connected subgraph(corresponding to triangulation). Finding cubic subgraph in planar graph is NP-complete. I see some connection.
Jan
8
awarded  Autobiographer
Jan
8
revised computational complexity
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Jan
8
revised computational complexity
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Jan
8
comment computational complexity
If we are given set of triangles as a certificate, first we will check connectivity, afterwards we check that the link of each vertex is a cycle. If these conditions are satisfied, we know for sure that we have a closed surface. Then calculate Euler characteristic, we are dealing with sphere if and only if Euler characteristic is 2. en.wikipedia.org/wiki/Surface#Classification_of_closed_surfaces here you can check what are the Euler characteristics of closed surfaces.
Jan
8
awarded  Student
Jan
8
revised computational complexity
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Jan
8
revised computational complexity
edited tags
Jan
8
revised computational complexity
edited tags