These are also called greedy algorithms Goals To recognize when simple dispatch rules apply To prove that they are the correct algorithm To analyze the running time of the algorithm brPage 2br Example 10 Questions What is the right algorithm What i ID: 25402
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1jjPCj Example:j pj 1 52 33 104 85 4Questions:Whatistherightalgorithm?Whatisitsrunningtime?Howdoweproveit? 1jjPCj Example:j pj 1 52 33 104 85 4Questions:Whatistherightalgorithm?{SPTWhatisitsrunningtime?{O(nlogn)Howdoweproveit? Basicformatofaninterchangeargument SpecifythesimpledispatchruleX.Assume,forthepurposedofcontradiction,thatyouhaveanoptimalschedulethatdoesnotobeytheruleX.FindtwospecicjobsjandkthatviolateruleX.Showthatifyouinterchangejobsjandk,then{Theresultingscheduleisstillfeasible.{Theobjectivefunctionvaluedoesnotincrease(foraminimizationproblem).Youcanthenconcludethat,viarepeatedswaps,theremustexistanoptimalschedulethatsatisedruleX.Comment:Eventhoughtheproofisboilerplate,youmustprovideenoughmathematicaldetailthatshowsthatyourproofappliestotheparticularproblemandtheparticularrule! 1jjPwjCj Example:j pj wj 1 1 12 3 23 7 14 10 20Questions:Howcanwegureoutasimpledispatchrule?Howdoweproveitiscorrect{ExchangeArgumentTwoanswerstorstquestion;Experimentwithsmallexamplesanddevelopaplausiblerule.Startanexchangeargumentandseewhatyouneedtomakeitwork. ProblemswithDeadlines DeadlinesCanbehard(deadlines)orsoft(duedates).ModelRealTimescheduling.Example1j pj dj 1 2 252 4 133 6 64 7 195 10 29Example2j pj dj 1 1 52 3 63 6 74 4 15 Whatifyoucan'tmeetalldeadlines: Onemetric:latenessLj=Cj�dj1jjLmaxInterpretation:ifLmaxis4,thenthereisascheduleinwhichnojobmissesitsdeadlinebymorethan4timeunits.Question:DoesEDDminimizeLmax?Answer: AddingReleaseDates.1jrjjLmax Question:DoesEDDstillproduceanoptimalschedule?j rj pj dj 1 4 1 52 0 4 6 Addingreleasedatestoacompletiontimeproblem. 1jrjjXCjExample1j rj pj 1 0 1002 40 1Example2j rj pj 1 0 1002 40 13 101 1