Thats a unique idea.You should consider the following idea to enhance your idea so that it would impact uniquely:  consider the problem of pattern matching with k mismatches, where there can be don't care or wild card characters in the pattern. Specifically, given a pattern P of length m and a text T of length n,  want to find all occurrences of P in T that have no more than k mismatches. The pattern can have don't care characters, which match any character. Without don't cares, the best known algorithm for pattern matching with k   mismatches has a runtime of O(nklog⁡k). With don't cares in the pattern, the best deterministic algorithm has a runtime of O(nkpolylogm). Therefore, there is an important gap beten the versions with and without don't cares.#R##N##R##N#  give an algorithm whose runtime increases with the number of don't cares.  define an island to be a maximal length substring of P that does not contain don't cares. Let q be the number of islands in P  .  present an algorithm that runs in O(nklog⁡m+nmin⁡{qklog2⁡m3,qlog⁡m}) time. If the number of islands q   is O(k)O(k) this runtime becomes O(nklog⁡m), which essentially matches the best known runtime for pattern matching with k mismatches without don't cares. If the number of islands q   is O(k2)O(k2), this algorithm is asymptotically faster than the previous best algorithm for pattern matching with k mismatches with don't cares in the pattern.
['Marius Nicolae', 'Sanguthevar Rajasekaran']
I am writing a research paper on a idea On pattern matching with k mismatches and few don't cares
[{"from": "human", "value": "I am writing a research paper on a idea On pattern matching with k mismatches and few don't cares"}, {"from": "gpt", "value": "Thats a unique idea.You should consider the following idea to enhance your idea so that it would impact uniquely:  consider the problem of pattern matching with k mismatches, where there can be don't care or wild card characters in the pattern. Specifically, given a pattern P of length m and a text T of length n,  want to find all occurrences of P in T that have no more than k mismatches. The pattern can have don't care characters, which match any character. Without don't cares, the best known algorithm for pattern matching with k \u00a0 mismatches has a runtime of O(nklog\u2061k). With don't cares in the pattern, the best deterministic algorithm has a runtime of O(nkpolylogm). Therefore, there is an important gap beten the versions with and without don't cares.#R##N##R##N#  give an algorithm whose runtime increases with the number of don't cares.  define an island to be a maximal length substring of P that does not contain don't cares. Let q be the number of islands in P \u00a0.  present an algorithm that runs in O(nklog\u2061m+nmin\u2061{qklog2\u2061m3,qlog\u2061m}) time. If the number of islands q \u00a0 is O(k)O(k) this runtime becomes O(nklog\u2061m), which essentially matches the best known runtime for pattern matching with k mismatches without don't cares. If the number of islands q \u00a0 is O(k2)O(k2), this algorithm is asymptotically faster than the previous best algorithm for pattern matching with k mismatches with don't cares in the pattern."}]