Thats a unique idea.You should consider the following idea to enhance your idea so that it would impact uniquely:  consider problems of distributing a number of points within a polygonal region P, such that the points are far away from each other. Problems of this type have been considered before for the case where the possible locations form a discrete set. Dispersion problems are closely related to packing problems. While Hochbaum and Maass [20] have given a polynomial-time approximation scheme for packing,  show that geometric dispersion problems cannot be approximated arbitrarily ll in polynomial time, unless P = NP. A special case of this observation solves an open problem by Rosenkrantz et al. [31].  give a 2/3 approximation algorithm for one version of the geometric dispersion problem. This algorithm is strongly polynomial in the size of the input, i.e., its running time does not depend on the area of P.  also discuss extensions and open problems.
['Christoph Baur', 'Sándor P. Fekete']
I am writing a research paper on a idea Approximation of geometric dispersion problems
[{"from": "human", "value": "I am writing a research paper on a idea Approximation of geometric dispersion problems"}, {"from": "gpt", "value": "Thats a unique idea.You should consider the following idea to enhance your idea so that it would impact uniquely:  consider problems of distributing a number of points within a polygonal region P, such that the points are far away from each other. Problems of this type have been considered before for the case where the possible locations form a discrete set. Dispersion problems are closely related to packing problems. While Hochbaum and Maass [20] have given a polynomial-time approximation scheme for packing,  show that geometric dispersion problems cannot be approximated arbitrarily ll in polynomial time, unless P = NP. A special case of this observation solves an open problem by Rosenkrantz et al. [31].  give a 2/3 approximation algorithm for one version of the geometric dispersion problem. This algorithm is strongly polynomial in the size of the input, i.e., its running time does not depend on the area of P.  also discuss extensions and open problems."}]