08 - NP-complete numerical problems- subset sum

# 08 - NP-complete numerical problems- subset sum - 30...

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3/31/08 - NP-complete numerical probl. .. NP-Complete Problems 3SAT Vtx Cover Indep. Set (even in deg 3) Clique Hamiltonian Path Set cover/packing Traveling salesman 3D matching Subset Sum. 3-D Matching Given sets X, Y, Z, with n elts each. Given 3-element sets S 1 , . .., S n . Each satisfes |S i X| = |S i Y| = |S i Z| = 1. “hypergraph” “hyperedges” Does a set oF hyperedges covering every vertex (i.e. element oF X Y Z) exactly once? Reduce From 3SAT “Variable gadgets” are pinwheels that can be in 2 confgs Gadget For x i “4” really denotes m, # clauses in the 3SAT Formula. These are the only hyperedges containing x i1 , . .., x im , y i1 , . .. y im Z,Z ̅ will belong to other hyp-edges There are exactly 2 ways to cover {x i1 , . .., x im , y i1 , . .., y im }. They correspond to setting x i = T, x i = ±, resp. The frst leaves every z ij exposed, the second leaves every z ̅ ij exposed.

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08 - NP-complete numerical problems- subset sum - 30...

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