Thats a unique idea.You should consider the following idea to enhance your idea so that it would impact uniquely:  revisit the complexity of one of the most basic problems in pattern matching. In the  k -mismatch problem  must compute the Hamming distance beten a pattern of length  m  and every  m -length substring of a text of length  n , as long as that Hamming distance is at most  k.  Where the Hamming distance is greater than  k  at some alignment of the pattern and text,  simply output "No".    study this problem in both the standard offline setting and also as a streaming problem. In the streaming  k -mismatch problem the text arrives one symbol at a time and  must give an output before processing any future symbols. Our main results are as follows:   • Our first result is a deterministic  O ( nk  2  log  k/m  +  n  polylog  m ) time  offline  algorithm for  k -mismatch on a text of length  n.  This is a factor of  k  improvement over the fastest previous result of this form from SODA 2000 [9, 10].   •  then give a randomised and online algorithm which runs in the same time complexity but requires only  O ( k  2  polylog  m ) space in total.   • Next  give a randomised (1 + e)-approximation algorithm for the streaming  k -mismatch problem which uses  O ( k  2  polylog  m /e 2 ) space and runs in  O (polylog  m /e 2 ) worst-case time per arriving symbol.   • Finally  combine our new results to derive a randomised  O ( k  2  polylog  m ) space algorithm for the streaming  k -mismatch problem which runs in  O ([EQUATION] log  k  + polylog  m ) worst-case time per arriving symbol. This improves the best previous space complexity for streaming  k -mismatch from FOCS 2009 [26] by a factor of  k.   also improve the time complexity of this previous result by an even greater factor to match the fastest known offline algorithm (up to logarithmic factors).
['Raphaël Clifford', 'Allyx Fontaine', 'Ely Porat', 'Benjamin Sach', 'Tatiana A. Starikovskaya']
I am writing a research paper on a idea The k -mismatch problem revisited
[{"from": "human", "value": "I am writing a research paper on a idea The k -mismatch problem revisited"}, {"from": "gpt", "value": "Thats a unique idea.You should consider the following idea to enhance your idea so that it would impact uniquely:  revisit the complexity of one of the most basic problems in pattern matching. In the  k -mismatch problem  must compute the Hamming distance beten a pattern of length  m  and every  m -length substring of a text of length  n , as long as that Hamming distance is at most  k.  Where the Hamming distance is greater than  k  at some alignment of the pattern and text,  simply output \"No\".    study this problem in both the standard offline setting and also as a streaming problem. In the streaming  k -mismatch problem the text arrives one symbol at a time and  must give an output before processing any future symbols. Our main results are as follows:   \u2022 Our first result is a deterministic  O ( nk  2  log  k/m  +  n  polylog  m ) time  offline  algorithm for  k -mismatch on a text of length  n.  This is a factor of  k  improvement over the fastest previous result of this form from SODA 2000 [9, 10].   \u2022  then give a randomised and online algorithm which runs in the same time complexity but requires only  O ( k  2  polylog  m ) space in total.   \u2022 Next  give a randomised (1 + e)-approximation algorithm for the streaming  k -mismatch problem which uses  O ( k  2  polylog  m /e 2 ) space and runs in  O (polylog  m /e 2 ) worst-case time per arriving symbol.   \u2022 Finally  combine our new results to derive a randomised  O ( k  2  polylog  m ) space algorithm for the streaming  k -mismatch problem which runs in  O ([EQUATION] log  k  + polylog  m ) worst-case time per arriving symbol. This improves the best previous space complexity for streaming  k -mismatch from FOCS 2009 [26] by a factor of  k.   also improve the time complexity of this previous result by an even greater factor to match the fastest known offline algorithm (up to logarithmic factors)."}]