Thats a unique idea.You should consider the following idea to enhance your idea so that it would impact uniquely: A tor is a sequence of simplicial complexes connected by simplicial maps.  show how to compute a filtration, a sequence of nested simplicial complexes, with the same persistent barcode as the tor. Our approach is based on the coning strategy by Dey et al. (SoCG 2014).  show that a variant of this approach yields a filtration that is asymptotically only marginally larger than the tor and can be efficiently computed by a streaming algorithm, both in theory and in practice. Furthermore,  show that our approach can be combined with a streaming algorithm to compute the barcode of the tor via matrix reduction. The space complexity of the algorithm does not depend on the length of the tor, but the maximal size of any subcomplex within the tor.
['Michael Kerber', 'Hannah Schreiber']
I am writing a research paper on a idea Barcodes of Towers and a Streaming Algorithm for Persistent Homology
[{"from": "human", "value": "I am writing a research paper on a idea Barcodes of Towers and a Streaming Algorithm for Persistent Homology"}, {"from": "gpt", "value": "Thats a unique idea.You should consider the following idea to enhance your idea so that it would impact uniquely: A tor is a sequence of simplicial complexes connected by simplicial maps.  show how to compute a filtration, a sequence of nested simplicial complexes, with the same persistent barcode as the tor. Our approach is based on the coning strategy by Dey et al. (SoCG 2014).  show that a variant of this approach yields a filtration that is asymptotically only marginally larger than the tor and can be efficiently computed by a streaming algorithm, both in theory and in practice. Furthermore,  show that our approach can be combined with a streaming algorithm to compute the barcode of the tor via matrix reduction. The space complexity of the algorithm does not depend on the length of the tor, but the maximal size of any subcomplex within the tor."}]