Thats a unique idea.You should consider the following idea to enhance your idea so that it would impact uniquely: Consider a sequence s_1,...,s_n of points in the plane.  want to find all maximal subsequences with a given hereditary property P: find for all indices i the largest index j^*(i)  such that s_i,...,s_{j^*(i)} has property P.  provide a general methodology that leads to the following specific results:#R##N##R##N#- In O(n log^2 n) time  can find all maximal subsequences with diameter at most 1. #R##N##R##N#- In O(n log n loglog n) time  can find all maximal subsequences whose convex hull has area at most 1.#R##N##R##N#- In O(n) time  can find all maximal subsequences that define monotone paths in some (subpath-dependent) direction.#R##N##R##N#The same methodology works for graph planarity, as follows. Consider a sequence of edges e_1,...,e_n over a vertex set V. In O(n log n) time  can find, for all indices i, the largest index j^*(i) such that (V,{e_i,..., e_{j^*(i)}}) is planar.
['Drago Bokal', 'Sergio Cabello', 'David Eppstein']
I am writing a research paper on a idea Finding All Maximal Subsequences with Hereditary Properties.
[{"from": "human", "value": "I am writing a research paper on a idea Finding All Maximal Subsequences with Hereditary Properties."}, {"from": "gpt", "value": "Thats a unique idea.You should consider the following idea to enhance your idea so that it would impact uniquely: Consider a sequence s_1,...,s_n of points in the plane.  want to find all maximal subsequences with a given hereditary property P: find for all indices i the largest index j^*(i)  such that s_i,...,s_{j^*(i)} has property P.  provide a general methodology that leads to the following specific results:#R##N##R##N#- In O(n log^2 n) time  can find all maximal subsequences with diameter at most 1. #R##N##R##N#- In O(n log n loglog n) time  can find all maximal subsequences whose convex hull has area at most 1.#R##N##R##N#- In O(n) time  can find all maximal subsequences that define monotone paths in some (subpath-dependent) direction.#R##N##R##N#The same methodology works for graph planarity, as follows. Consider a sequence of edges e_1,...,e_n over a vertex set V. In O(n log n) time  can find, for all indices i, the largest index j^*(i) such that (V,{e_i,..., e_{j^*(i)}}) is planar."}]