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10. (7 points) In class we saw a in poly-time reduction from 3D Matching to Subset Sum. Recall that the 3D Matching problem gives you groups of three (aka "triples") to choose from, where each triple has one element from each of three different sets, X,Y, and Z, and then asks whether a subset M of the given triples T can be chosen so that each element of XYZ is in exactly one triple of M, thus forming a so-called "perfect 3D matching". 3D-matching p Subset Sum I.e., Subset Sum can solve the 3D-matching Problem Construction. Let XYZ be a instance of 3D-MATCHING with set T of triples, Let n=X=Y=Z and m=T. - Let X={x1,x2,x1,x4},Y={y1,y2,yy,y4},z={z1,zzzyz4} - For each triple t=(x,y1,zk)T, create an integer wt, with digits that has a 1 in positions ++and 2n+. Claim. There is a perfect 3D matching iff some subset sums to W= (a) Complete the blanks in the figure/slide and table above to illustrate the reduction of the above 3D matching instance into a corresponding subset sum instance. 10. (7 points) In class we saw a in poly-time reduction from 3D Matching to Subset Sum. Recall that the 3D Matching problem gives you groups of three (aka "triples") to choose from, where each triple has one element from each of three different sets, X,Y, and Z, and then asks whether a subset M of the given triples T can be chosen so that each element of XYZ is in exactly one triple of M, thus forming a so-called "perfect 3D matching". 3D-matching p Subset Sum I.e., Subset Sum can solve the 3D-matching Problem Construction. Let XYZ be a instance of 3D-MATCHING with set T of triples, Let n=X=Y=Z and m=T. - Let X={x1,x2,x1,x4},Y={y1,y2,yy,y4},z={z1,zzzyz4} - For each triple t=(x,y1,zk)T, create an integer wt, with digits that has a 1 in positions ++and 2n+. Claim. There is a perfect 3D matching iff some subset sums to W= (a) Complete the blanks in the figure/slide and table above to illustrate the reduction of the above 3D matching instance into a corresponding subset sum instance