Thats a unique idea.You should consider the following idea to enhance your idea so that it would impact uniquely: Given two finite sets of points X + and X − in R d ,t he maximum box problem is the problem of finding a box (hyperrectangle) B = {x : l ≤ x ≤ u} such that B ∩ X − = ∅, and the cardinality of B ∩ X + is maximized. The maximum bichromatic discrepancy problem is to find a box B maximizing the difference beten the number of the points of X + and X − inside the box, i.e. max ||B ∩ X + |−| B ∩ X − ||. ,  discuss an exact algorithm for the maximum box problem on the plane. In addition,  provide factor 2 approximation algorithms for planar cases of both problems and give an extension to the numerical discrepancy problem.
['Ying Liu', 'Mikhail Nediak']
I am writing a research paper on a idea Planar Case of the Maximum Box and Related Problems
[{"from": "human", "value": "I am writing a research paper on a idea Planar Case of the Maximum Box and Related Problems"}, {"from": "gpt", "value": "Thats a unique idea.You should consider the following idea to enhance your idea so that it would impact uniquely: Given two finite sets of points X + and X \u2212 in R d ,t he maximum box problem is the problem of finding a box (hyperrectangle) B = {x : l \u2264 x \u2264 u} such that B \u2229 X \u2212 = \u2205, and the cardinality of B \u2229 X + is maximized. The maximum bichromatic discrepancy problem is to find a box B maximizing the difference beten the number of the points of X + and X \u2212 inside the box, i.e. max ||B \u2229 X + |\u2212| B \u2229 X \u2212 ||. ,  discuss an exact algorithm for the maximum box problem on the plane. In addition,  provide factor 2 approximation algorithms for planar cases of both problems and give an extension to the numerical discrepancy problem."}]