Thats a unique idea.You should consider the following idea to enhance your idea so that it would impact uniquely:  study the problem of discrete geometric packing. Here, given ighted regions (say in the plane) and points (with capacities), one has to pick a maximum ight subset of the regions such that no point is covered more than its capacity.  provide a general framework and an algorithm for approximating the optimal solution for packing in hypergraphs arising out of such geometric settings. Using this framework  get a flotilla of results on this problem (and also on its dual, where one wants to pick a maximum ight subset of the points when the regions have capacities). For example, for the case of fat triangles of similar size,  show an (1)-approximation and prove that no PTAS is possible. See [ehr-gpnuc-11] for the full version of the paper.
['Alina Ene', 'Sariel Har-Peled', 'Benjamin Raichel']
I am writing a research paper on a idea Geometric packing under non-uniform constraints
[{"from": "human", "value": "I am writing a research paper on a idea Geometric packing under non-uniform constraints"}, {"from": "gpt", "value": "Thats a unique idea.You should consider the following idea to enhance your idea so that it would impact uniquely:  study the problem of discrete geometric packing. Here, given ighted regions (say in the plane) and points (with capacities), one has to pick a maximum ight subset of the regions such that no point is covered more than its capacity.  provide a general framework and an algorithm for approximating the optimal solution for packing in hypergraphs arising out of such geometric settings. Using this framework  get a flotilla of results on this problem (and also on its dual, where one wants to pick a maximum ight subset of the points when the regions have capacities). For example, for the case of fat triangles of similar size,  show an (1)-approximation and prove that no PTAS is possible. See [ehr-gpnuc-11] for the full version of the paper."}]