PDF-LeftistHeaps|OverviewOurgoalistobeabletomergetwoheapsinO(logn)time,wh

Exercises1Explainhowmergecanbeusedtoimplementinsertanddeleteminandthenwritecodetodoso2Showthestateofaleftistheapattheendofinsert123456deletemininsert78deletemindeletemin4. logn).Thisproblemoflearningparitywithnoiseis,increasingly,understoodtobeacentralprobleminlearningtheory.Addi-tionally,thisproblemreoccursinvariousformsinseveralareasoftheoreticalcomputerscience,includ 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. Klogn n(1)thenthenetworkisconnectedwithhighprobability,whileitislikelytobedisconnectedbelowthisthreshold.Inthispaperweconsideranextremelyseverekindofmas-siveattack.Theadversaryselectsacertainnumberof Programming Abstractions in C++. Cynthia . Bailey Lee. .  .              . CS2 in C++ Peer Instruction Materials by . Cynthia Bailey Lee.  is licensed under a . Creative Commons Attribution-. V nQ1()+Ologn n:(2)Here,Q1(
)denotestheinverseoftheGaussianQ-functionQ(x),Z1x1 p 2et2=2dt(3)andVisthechanneldispersion[9,Def.1].Theapproxima-tion(2)impliesthattosustainthedesirederrorprobabilit wlogn+n2 "
logn+"n3time.Unfortunatelythebestknownupperboundforfisf(")=O(1=(log1="))forsome0(cf.Section2.1).For"=1=p n,weobtainaverymodestruntimeimprove-mentoverFourRussians.Howevernomajorimpedime 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"fractionofallconstraintsissatisable.RecentlyTrevisan[17]developedanalgorithmthatsatises1O(3p "logn)fractionofallconstraints(thiscanbeimprovedto1O(p "logn)[9]) Reading: Chapter 2. 2. Complexity Analysis. Measures efficiency (time and memory) of algorithms and programs. Can be used for the following. Compare different algorithms. See how time varies with size of the input. k
n3=2)factor;thisisonlyap kfactorlooserthanthatof[25].Oursecondapplicationisacollectionofvarioushierarchicalidentity-basedencryp-tion(HIBE)schemes,whicharetherstHIBEsthatdonotrelyonbilinearpai Howeverbyabriefcomputationweseethatno2-stateDFAcanseparatethesetwowordsSosep100000103Notethatsepwxsepxwbe-causethelanguageofaDFAcanbecomplementedbyswappingtherejectandacceptstatesWeletSnmaxw6xjwjjxjns What is . Pathfinding. ?. Find a path between two given locations on a map with obstacles. A Broad Area with Many Types of .... A Challenging Search Problem. Need solution in real time. CPU and memory resources are often limited.