Thats a unique idea.You should consider the following idea to enhance your idea so that it would impact uniquely:  give a number of new lor bounds in the cell probe model with logarithmic cell size, which entails the same bounds on the random access computer with logarithmic word size and unit cost operations.  study the signed prefix sum problem: given a string of length n of zeroes and signed ones, compute the sum of its ith prefix during updates.  show a lor bound of  Omega(log n/log log n) time per operations, even if the prefix sums are bounded by log n/log log n during all updates.  also show that if the update time is bounded by the product of the worst-case update time and the ansr to the query, then the update time must be Omega(sqrt(log n/ log log n)).  These results allow us to prove lor bounds for a variety of seemingly unrelated dynamic problems.  give a lor bound for the dynamic planar point location in monotone subdivisions of  Omega(log n/ log log n) per operation.  give a lor bound for the dynamic transitive closure problem on upward planar graphs with one source and one sink of  Omega(log n/(log logn)^2) per operation.  give a lor bound of  Omega(sqrt(log n/log log n)) for the dynamic membership problem of any Dyck language with two or more letters. This implies the same lor bound for the dynamic word problem for the free group with k generators.  also give lor bounds for the dynamic prefix majority and prefix equality problems.
['Thore Husfeldt', 'Theis Rauhe', 'Søren Skyum']
I am writing a research paper on a idea Lower Bounds for Dynamic Transitive Closure, Planar Point Location, and Parentheses Matching
[{"from": "human", "value": "I am writing a research paper on a idea Lower Bounds for Dynamic Transitive Closure, Planar Point Location, and Parentheses Matching"}, {"from": "gpt", "value": "Thats a unique idea.You should consider the following idea to enhance your idea so that it would impact uniquely:  give a number of new lor bounds in the cell probe model with logarithmic cell size, which entails the same bounds on the random access computer with logarithmic word size and unit cost operations.  study the signed prefix sum problem: given a string of length n of zeroes and signed ones, compute the sum of its ith prefix during updates.  show a lor bound of\u00a0 Omega(log n/log log n) time per operations, even if the prefix sums are bounded by log n/log log n during all updates.  also show that if the update time is bounded by the product of the worst-case update time and the ansr to the query, then the update time must be Omega(sqrt(log n/ log log n)).  These results allow us to prove lor bounds for a variety of seemingly unrelated dynamic problems.  give a lor bound for the dynamic planar point location in monotone subdivisions of  Omega(log n/ log log n) per operation.  give a lor bound for the dynamic transitive closure problem on upward planar graphs with one source and one sink of  Omega(log n/(log logn)^2) per operation.  give a lor bound of\u00a0 Omega(sqrt(log n/log log n)) for the dynamic membership problem of any Dyck language with two or more letters. This implies the same lor bound for the dynamic word problem for the free group with k generators.  also give lor bounds for the dynamic prefix majority and prefix equality problems."}]