Domande primo parziale optimization and data scienceo

Definition

· : With Al INI 11-m withGIN andandguapedirectedconsider man un = ,,j)associated A5) /iwith 11quezij ,,The withto tweerubblems subgwapeestask find minimum ispanning a e a.,, .theAll with puspertiesTN following :, commente d1 . cyelio2 a. with /Al.3 1n -=withe .minimum costam with polynonialformulation constraintsnumber of· :min dijyijri si ex, bi=fh1 ifwithVienbiillea si. is =videa 1859VjeNYij 1Vistea . Arj)V/iQyijXij ,19&20 j) A/i eYij , ,j) -Ar/i20Xij ,

Algolithum Knuskal's

· To withthe respectnon-becreasingsouting costauberin Lof -aues twee* emptystart0· Il from an= /(m-1)/I +* doWhile· first itemthe j)select L3/iin· ,51)(19/iL· ,= */T j)(i syelioIf isU· a,↑* * j)T U (i= ,endwhile

Optimality condition

· : The #*free cost twee onlyspanningspanning andis minimum ififaovem : atheit optimalitysatisfies conditionsfollowing :*,V *j) effet obtainedoutwhere the/i is/K&T whenofsijee arean,, **/i j) removedis gram,

Mathematical formulation

GiXi· maxi : ex mt set items11V of,· = ..., itemutility :Eb ofe·Six :ier itemweight :ofa·19Xieg0 Vien Knapsackb capacity·, to item selectedbinally variable when i isequal-Xi one ,,otherwise

Oalgorithm Dynamic mungwamming

· : Table blielementbuild whichwith and bWe columns jD in+1a rowsn ,, theobtained girstrepresents that onlywhenthe utility itemsbe imaximum can forthe the jcapacity equalKnapsackandconsidered ismaximum ofare .The equation boldfollowing maxyb/i ai))1)& b/i jj)(i + 1ci -= - - ,,, i/0if se51111barie :case =,

Problem equivalence

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