Thats a unique idea.You should consider the following idea to enhance your idea so that it would impact uniquely:  show that in the document exchange problem, where Alice holds x e {0, 1}n and Bob holds y e {0, 1}n, Alice can send Bob a message of size O(K(log2 K + log n)) bits such that Bob can recover x using the message and his input y if the edit distance beten x and y is no more than K, and output "error" otherwise. Both the encoding and decoding can be done in time O(n + poly(K)). This result significantly improves on the previous communication bounds under polynomial encoding/decoding time.  also show that in the referee model, where Alice and Bob hold x and y respectively, they can compute sketches of x and y of sizes poly(K log n) bits (the encoding), and send to the referee, who can then compute the edit distance beten x and y together with all the edit operations if the edit distance is no more than K, and output "error" otherwise (the decoding). To the best of our knowledge, this is the first result for sketching edit distance using poly(K log n) bits. Moreover, the encoding phase of our sketching algorithm can be performed by scanning the input string in one pass. Thus our sketching algorithm also implies the first streaming algorithm for computing edit distance and all the edits exactly using poly(K log n) bits of space.
['Djamal Belazzougui', 'Qin Zhang']
I am writing a research paper on a idea Edit Distance: Sketching, Streaming, and Document Exchange
[{"from": "human", "value": "I am writing a research paper on a idea Edit Distance: Sketching, Streaming, and Document Exchange"}, {"from": "gpt", "value": "Thats a unique idea.You should consider the following idea to enhance your idea so that it would impact uniquely:  show that in the document exchange problem, where Alice holds x e {0, 1}n and Bob holds y e {0, 1}n, Alice can send Bob a message of size O(K(log2 K + log n)) bits such that Bob can recover x using the message and his input y if the edit distance beten x and y is no more than K, and output \"error\" otherwise. Both the encoding and decoding can be done in time O(n + poly(K)). This result significantly improves on the previous communication bounds under polynomial encoding/decoding time.  also show that in the referee model, where Alice and Bob hold x and y respectively, they can compute sketches of x and y of sizes poly(K log n) bits (the encoding), and send to the referee, who can then compute the edit distance beten x and y together with all the edit operations if the edit distance is no more than K, and output \"error\" otherwise (the decoding). To the best of our knowledge, this is the first result for sketching edit distance using poly(K log n) bits. Moreover, the encoding phase of our sketching algorithm can be performed by scanning the input string in one pass. Thus our sketching algorithm also implies the first streaming algorithm for computing edit distance and all the edits exactly using poly(K log n) bits of space."}]