Question: Consider the following problem, called BOXDEPTH: Given a set of n axis-aligned rectangles in the plane, how big is the largest subset of these rectangles

Consider the following problem, called BOXDEPTH: Given a set of n axis-aligned rectangles in the plane, how big is the largest subset of these rectangles that contain a common point?

(a) Describe a polynomial-time reduction from BOXDEPTH to MAXCLIQUE.

(b) Describe and analyze a polynomial-time algorithm for BOXDEPTH. [Hint: O(n3) time should

be easy, but O(n log n) time is possible.]

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