08 - Greedy Scheduling Algorithms

# 08 Greedy - “Greedy stays ahead” Prop ∀ k ≥ 0 I± the “earliest completion time” alg ²nishes its k-th job at time t then no ±easible

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1/25/08 - Greedy Scheduling Algorithms Lecture: Greedy scheduling algorithms Reading: Chapter 4.1, 4.2 Interval Scheduling (“jobs”) Input: A set of pairs (si, ti) T i=1 0 s i t i T, s i , t i N Output: A feasible schedule: a subset of the pairs, s.t. the intervals are disjoint Goal: Max. number of jobs (s 1 , t 1 ) and (s 2 , t 2 ) are disjoint if s 2 > t 1 (2, 3) and (3, 4) cannot coexist (1) Earliest start time - can be arbitrarily far from optimal (2) Shortest jobs Frst 5-1 5

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(3) Fewest conficts (4) Earliest start time with pre-emption (5) Brute ±orce search. exp time Proo± o± (6) Earliest completion time
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Unformatted text preview: “Greedy stays ahead” Prop. ∀ k ≥ 0 I± the “earliest completion time” alg ²nishes its k-th 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 (k-1)th job at t’. By hypothesis no sched. ²nishes k-1 jobs < t’. Among jobs that start a±ter t’, ECT is ²nishing as soon as possible. Corollary. ECT produces an optimal ±easible schedule. 5-2...
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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).

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08 Greedy - “Greedy stays ahead” Prop ∀ k ≥ 0 I± the “earliest completion time” alg ²nishes its k-th job at time t then no ±easible

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