Nesting boxes A d-dimensional box with dimensions .x1;
Chapter 24, Problem 24-2(choose chapter or problem)
Nesting boxes A d-dimensional box with dimensions .x1; x2;:::;xd / nests within another box with dimensions .y1; y2;:::;yd / if there exists a permutation on f1; 2; : : : ; dg such that x.1/ < y1, x.2/ < y2,..., x.d / < yd . a. Argue that the nesting relation is transitive. b. Describe an efficient method to determine whether or not one d-dimensional box nests inside another. c. Suppose that you are given a set of n d-dimensional boxes fB1; B2;:::;Bng. Give an efficient algorithm to find the longest sequence hBi1; Bi2 ;:::;Bik i of boxes such that Bij nests within BijC1 for j D 1; 2; : : : ; k 1. Express the running time of your algorithm in terms of n and d.
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