Computers and Technology, 30.11.2019 02:31 sardarp1irc5

Describe an efficient algorithm that, given a set {x1, } of points on the real line, determines the smallest set of unit-length closed intervals that contains all of the given points. (a unit length interval just means any closed interval with length 1. i. e., an interval [a, b] where b − a = 1.)
a. briefly describe a greedy algorithm for the unit length interval problem.
b. state and prove a "swapping lemma" for your greedy algorithm.
c. write a proof that uses your swapping lemma to show that your greedy algorithm does indeed produce a set of intervals that contain all of the points {x1, } with the fewest number of intervals.

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Describe an efficient algorithm that, given a set {x1, } of points on the real line, determines the...

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