Thats a unique idea.You should consider the following idea to enhance your idea so that it would impact uniquely:  show how to determine whether the edit distance beten two given strings is small in sublinear time. Specifically,  present a test which, given two n-character strings A and B, runs in time o(n) and with high probability returns " CLOSE " if their edit distance is O(n Α ), and " FAR " if their edit distance is Ω(n), where Α is a fixed parameter less than 1. Our algorithm for testing the edit distance works by recursively subdividing the strings A and B into smaller substrings and looking for pairs of substrings in A, B with small edit distance. To do this,  query both strings at random places using a special technique for economizing on the samples which does not pick the samples independently and provides better query and overall complexity. As a result, our test runs in time O(n max(Α/2, 2Α - 1\) ) for any fixed Α  Α/2 ) on the query complexity of every algorithm that distinguishes pairs of strings with edit distance at most n Α  from those with edit distance at least n/6.
['Tugkan Batu', 'Funda Ergün', 'Joe Kilian', 'Avner Magen', 'Sofya Raskhodnikova', 'Ronitt Rubinfeld', 'Rahul Sami']
I am writing a research paper on a idea A sublinear algorithm for weakly approximating edit distance
[{"from": "human", "value": "I am writing a research paper on a idea A sublinear algorithm for weakly approximating edit distance"}, {"from": "gpt", "value": "Thats a unique idea.You should consider the following idea to enhance your idea so that it would impact uniquely:  show how to determine whether the edit distance beten two given strings is small in sublinear time. Specifically,  present a test which, given two n-character strings A and B, runs in time o(n) and with high probability returns \" CLOSE \" if their edit distance is O(n \u0391 ), and \" FAR \" if their edit distance is \u03a9(n), where \u0391 is a fixed parameter less than 1. Our algorithm for testing the edit distance works by recursively subdividing the strings A and B into smaller substrings and looking for pairs of substrings in A, B with small edit distance. To do this,  query both strings at random places using a special technique for economizing on the samples which does not pick the samples independently and provides better query and overall complexity. As a result, our test runs in time O(n max(\u0391/2, 2\u0391 - 1\\) ) for any fixed \u0391  \u0391/2 ) on the query complexity of every algorithm that distinguishes pairs of strings with edit distance at most n \u0391  from those with edit distance at least n/6."}]