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Algorithms for persistent homology and zigzag persistent homology are well-studied for persistence modules where homomorphisms are induced by inclusion maps.
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2011
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C. Chen and M. Kerber. An output-sensitive algorithm for persistent homology. Proc. 27th Annu. Sympos. Comput. Geom
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T. K. Dey, J. Sun, and Y. Wang. Approximating cycles in a shortest basis of the first homology group from point data. Inverse Problems
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J.-D. Boissonnat, T. K. Dey, and C. Maria. The compressed annotation matrix: An efficient data structure for computing persistent cohomology. Proc. European Sympos. Algorithms
2013
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Topological persistence for circle-valued maps
D. Burghelea and T. K. Dey · 2013
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T. K. Dey, F. Fan, and Y. Wang. Graph Induced Complex on Point Data. Proc. 29th Annu. Sympos. Comput. Geom
2013
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