Thats a unique idea.You should consider the following idea to enhance your idea so that it would impact uniquely: The (Vietoris-)Rips complex of a discrete point-set  P  is an abstract simplicial complex in which a subset of  P  defines a simplex if and only if the diameter of that subset is at most 1.  describe an efficient algorithm to determine whether a given cycle in a planar Rips complex is contractible. Our algorithm requires  O ( m  log  n ) time to preprocess a set of  n  points in the plane in which  m  pairs have distance at most 1; after preprocessing, deciding whether a cycle of  k  Rips edges is contractible requires  O ( k ) time.  also describe an algorithm to compute the shortest non-contractible cycle in a planar Rips complex in  O ( n  2 log  n  +  mn ) time.
['Erin W. Chambers', 'Jeff Erickson', 'Pratik Worah']
I am writing a research paper on a idea Testing contractibility in planar rips complexes
[{"from": "human", "value": "I am writing a research paper on a idea Testing contractibility in planar rips complexes"}, {"from": "gpt", "value": "Thats a unique idea.You should consider the following idea to enhance your idea so that it would impact uniquely: The (Vietoris-)Rips complex of a discrete point-set  P  is an abstract simplicial complex in which a subset of  P  defines a simplex if and only if the diameter of that subset is at most 1.  describe an efficient algorithm to determine whether a given cycle in a planar Rips complex is contractible. Our algorithm requires  O ( m  log  n ) time to preprocess a set of  n  points in the plane in which  m  pairs have distance at most 1; after preprocessing, deciding whether a cycle of  k  Rips edges is contractible requires  O ( k ) time.  also describe an algorithm to compute the shortest non-contractible cycle in a planar Rips complex in  O ( n  2 log  n  +  mn ) time."}]