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1IntroductionThecontributionofthispaperistwo-fold.First,wedeneanewcla

1IntroductionThecontributionofthispaperistwo-fold.First,wedeneanewcla

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logN)simultaneouslyhardcorebits(whereNisthelengtho...

Delete(x):thisremovesthekeyfromthesetS,i.e.,S:=S�fxg.Pre xSearch(x):th

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allowsthesystemtoexecutePre xSearch(x),Insert(x)an...

constant1=2,givenO(n)examples,withhighprobabilitytherewillonlybeonese

constant1=2,givenO(n)examples,withhighprobabilitytherewillonlybeonese

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logn).Thisproblemoflearningparitywithnoiseis,incre...

LeftistTrees

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Figure1:AtypicalroundofMastermindacolorcombinationoffourpegs.Eachpegca

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lowerboundof (nlogk=logn)foranyk=k(n).Extendingthe...

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Algorithms. Chapter 3. Growth of Functions. Credi...

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locationusingtheoverlaygraphisdoneinthesevariousnetworksbyusingdi eren

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logn)fractionofthenodeschosenbyanadversarystilllea...

pected(k2n1=k)processingtimeperedge.Notethatthesizeofthespannerthusco

pected(k2n1=k)processingtimeperedge.Notethatthesizeofthespannerthusco

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logn loglogn)worstcasebound.Anotherdifferenceistha...

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Finally,ifnoneoftheabovehappens,thesetsB(x;31)and...

c(H)suchthat,foreachsetpair(Si;Ti),thereareatleastkiedge-disjointpaths

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edges)withlargeprobability.Thisleadstothefollowing...

experimentally.Oneofthemaincontributionsofthispaperistoshowthattheycan

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Klogn n(1)thenthenetworkisconnectedwithhighprobab...

forVertexCoverwiththesameapproximationfactor2� (1

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p logn)asinthebestknownapproximationalgorithmforVe...

thedirectedgraph(whereseparatedirectededgeswouldrepresentTimsendingane

thedirectedgraph(whereseparatedirectededgeswouldrepresentTimsendingane

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Wechoosek=(2+)lognattacknodesforasmallpositivean...

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2 logn n)[5]. Fig.3.Spatialreusein(a)half-duplexan...

thefollowingexample.Example1.1.Considerthesequenceofvaluesa,a,b,b,b,a,

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n=numberoftherunsinthesequence RepresentationSchem...

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theoreticoptimum.WewillprovethematchinglowerboundinSection5.Aninterest

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logn)factorofthebestsuchlowerboundinthenon-stochas...

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wlogn+n2 "logn+"n3time.Unfortunatelythebestknown...

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log(1="))fractionofallconstraintsif1"fractionofal...

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logn)nodesbytheat-tackerinann-nodenetworkcanbeginc...

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(logn),ourresultrequires

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kn3=2)factor;thisisonlyap kfactorlooserthantha...

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ThisresearchwaspartlysupportedbyDFGgrantsBO275...

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wesearchpfromtheleftboundaryoftheintervalIfpisinth...

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