PDF-LeftistHeaps|OverviewOurgoalistobeabletomergetwoheapsinO(logn)time,wh

Author : alexa-scheidler | Published Date : 2017-01-30

Exercises1Explainhowmergecanbeusedtoimplementinsertanddeleteminandthenwritecodetodoso2Showthestateofaleftistheapattheendofinsert123456deletemininsert78deletemindeletemin4

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LeftistHeaps|OverviewOurgoalistobeabletomergetwoheapsinO(logn)time,wh: Transcript

Exercises1Explainhowmergecanbeusedtoimplementinsertanddeleteminandthenwritecodetodoso2Showthestateofaleftistheapattheendofinsert123456deletemininsert78deletemindeletemin4. CS-130AWBLT1' &$ % Linkedbinarytrees.InsertandDeleteMin(orDeleteMax)takesO(logn)time.CanMeld(Merge)twoleftisttreesinO(logn)time. CS-130AWBLT2' &$ % ExtendedBinaryTrees (Addexternalnodes) CS-130AWBL Algorithms. Chapter 3. Growth of Functions. Credit. : Dr. George . Bebis. 2. Analysis of Algorithms. Goal. :. To analyze and compare . algorithms . in . terms of . running time. . and . memory requirements. p logn)asinthebestknownapproximationalgorithmforVertexCoverbyKarakostas[11].ThepreviouslybestknownapproximationratioforMinUnCutisO(logn)[9],andthebestpreviouslyknownap-proximationforMin2CNFDeletionisO Inlecture19,wesawanLPrelaxationbasedalgorithmtosolvethesparsestcutproblemwithanapproximationguaranteeofO(logn).Inthislecture,wewillshowthattheintegralitygapoftheLPrelaxationisO(logn)andhencethisistheb Fromthescalinglaw,weobservethefollowingscalinglimitsonthepermissiblesparsityintermsofthedimensionalityofthesearchspace:kontheorderof1=)kvk0.n=p logn(6)kontheorderofn=)kvk0.p n=p logn(7)Thatis,asearchs log(1="))fractionofallconstraintsif1"fractionofallconstraintsissatisable.RecentlyTrevisan[17]developedanalgorithmthatsatises1O(3p "logn)fractionofallconstraints(thiscanbeimprovedto1O(p "logn)[9]) Richard Peng. Georgia Tech. Rasmus Kyng. Yale. Sushant Sachdeva. Google .  U of Toronto. Jakub Pachocki. Harvard. Graph Sparsification. The Resparsification Game. Concentration bounds. (Matrix) Martingales. kn3=2)factor;thisisonlyap kfactorlooserthanthatof[25].Oursecondapplicationisacollectionofvarioushierarchicalidentity-basedencryp-tion(HIBE)schemes,whicharetherstHIBEsthatdonotrelyonbilinearpai ThisresearchwaspartlysupportedbyDFGgrantsBO2755/1-1andSO514/4-3andwithintheCollaborativeResearchCenterSFB876,projectA2.Thenalauthenticatedversionisavailableonlineathttps://doi.org/10.1007/978 wesearchpfromtheleftboundaryoftheintervalIfpisinthesecondhalfpartofthecriticalintervalwesearchpfromtherightboundarySearchinginthiswayisnotonlyacon-siderationofefficiencybutveryimportanttomaintainprope 26underwhichamalicioususercancreatemultiplefakeOSNaccountsTheproblemIthasbeenreportedthat15millionfakeorcompromisedFacebookaccountswereonsaleduringFebruary20107FakeSybilOSNaccountscanbeusedforvariousp Howeverbyabriefcomputationweseethatno2-stateDFAcanseparatethesetwowordsSosep100000103Notethatsepwxsepxwbe-causethelanguageofaDFAcanbecomplementedbyswappingtherejectandacceptstatesWeletSnmaxw6xjwjjxjns processorstoagreementalargemajoritybutnotnecessarilyallgoodprocessorsarebroughttoagreement13ResultsWeusethephrasewithhighprobabilitywhptomeanthataneventhappenswithprobabilityatleast101ncforeveryconsta min(jSj;jSj);whereS=VnSandE(S;S)isthenumberofcutedges,thatis,thenumberofedgesfromStoS.TheSparsestCutproblemaskstondacut(S;S)withsmallestpossiblesparsity(S).Wedenotet

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