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Unformatted text preview: “Greedy stays ahead” Prop. ∀ k ≥ 0 I± the “earliest completion time” alg ²nishes its kth job at time t, then no ±easible sched. ²nishes k jobs be±ore t. Proo±. Induction on k. Base case: k = 0: trivial Ind. step. Suppose ECT alg ²nishes kth job at t, and (k1)th job at t’. By hypothesis no sched. ²nishes k1 jobs < t’. Among jobs that start a±ter t’, ECT is ²nishing as soon as possible. Corollary. ECT produces an optimal ±easible schedule. 52...
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This note was uploaded on 10/02/2008 for the course CS 482 taught by Professor Kleinberg during the Spring '08 term at Cornell University (Engineering School).
 Spring '08
 KLEINBERG
 Algorithms

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