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• W2025885831 abstract "Sampling conditions for recovering the homology of a set using topological persistence are much weaker than sampling conditions required by any known polynomial time algorithm for producing a topologically correct reconstruction. Under the former sampling conditions which we call weak sampling conditions, we give an algorithm that outputs a topologically correct reconstruction. Unfortunately, even though the algorithm terminates, its time complexity is unbounded. Motivated by the question of knowing if a polynomial time algorithm for reconstruction exists under the weak sampling conditions, we identify at the heart of our algorithm a test which requires answering the following question: given two 2-dimensional simplicial complexes L ⊂ K, does there exist a simplicial complex containing L and contained in K which realizes the persistent homology of L into K? We call this problem the homological simplification of the pair (K, L) and prove that this problem is NP-complete, using a reduction from 3SAT." @default.
• W2025885831 created "2016-06-24" @default.
• W2025885831 creator A5021546111 @default.
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• W2025885831 date "2010-06-13" @default.
• W2025885831 modified "2023-10-13" @default.
• W2025885831 title "Optimal reconstruction might be hard" @default.
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• W2025885831 doi "https://doi.org/10.1145/1810959.1811014" @default.
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