Thats a unique idea.You should consider the following idea to enhance your idea so that it would impact uniquely: Given a set of geometric objects each associated with a time value,  wish to determine whether a given property is true for a subset of those objects whose time values fall within a query time window.  call such problems time-windod decision problems, and they have been the subject of much recent attention, for instance studied by Bokal, Cabello, and Eppstein [SoCG 2015]. ,  present new approaches to this class of problems that are conceptually simpler than Bokal et al.'s, and also lead to faster algorithms. For instance,  present algorithms for preprocessing for the time-windod 2D diameter decision problem in O(n log n) time and the time-windod 2D convex hull area decision problem in O(n alpha(n) log n) time (where alpha is the inverse Ackermann function), improving Bokal et al.'s O(n log^2 n) and O(n log n loglog n) solutions respectively.#R##N##R##N#Our first approach is to reduce time-windod decision problems to a generalized range successor problem, which  solve using a novel way to search range trees. Our other approach is to use dynamic data structures directly, taking advantage of a new observation that the total number of combinatorial changes to a planar convex hull is near linear for any FIFO update sequence, in which deletions occur in the same order as insertions.  also apply these approaches to obtain the first O(n polylog n) algorithms for the time-windod 3D diameter decision and 2D orthogonal segment intersection detection problems.
['Timothy M. Chan', 'Simon Pratt']
I am writing a research paper on a idea Two Approaches to Building Time-Windowed Geometric Data Structures.
[{"from": "human", "value": "I am writing a research paper on a idea Two Approaches to Building Time-Windowed Geometric Data Structures."}, {"from": "gpt", "value": "Thats a unique idea.You should consider the following idea to enhance your idea so that it would impact uniquely: Given a set of geometric objects each associated with a time value,  wish to determine whether a given property is true for a subset of those objects whose time values fall within a query time window.  call such problems time-windod decision problems, and they have been the subject of much recent attention, for instance studied by Bokal, Cabello, and Eppstein [SoCG 2015]. ,  present new approaches to this class of problems that are conceptually simpler than Bokal et al.'s, and also lead to faster algorithms. For instance,  present algorithms for preprocessing for the time-windod 2D diameter decision problem in O(n log n) time and the time-windod 2D convex hull area decision problem in O(n alpha(n) log n) time (where alpha is the inverse Ackermann function), improving Bokal et al.'s O(n log^2 n) and O(n log n loglog n) solutions respectively.#R##N##R##N#Our first approach is to reduce time-windod decision problems to a generalized range successor problem, which  solve using a novel way to search range trees. Our other approach is to use dynamic data structures directly, taking advantage of a new observation that the total number of combinatorial changes to a planar convex hull is near linear for any FIFO update sequence, in which deletions occur in the same order as insertions.  also apply these approaches to obtain the first O(n polylog n) algorithms for the time-windod 3D diameter decision and 2D orthogonal segment intersection detection problems."}]