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NP-complete

 Bin packing
 Clique 
 Dominating set
 Exact cover by 3-sets
 Graph 3-colorability
 Hamiltonian cycle
 Integer linear programming
 Longest path
 Minimum broadcast time
 Minimum cover
 Multiprocessor scheduling
 Partition 
 Partition into cliques
 Precedence-constrained scheduling
 Regex matching with backreferences
 Satisfiability
 Subgraph isomorphism
 Subset-sum
 3-dimensional matching
 Travelling salesman
 Vertex cover
 ... (hundreds more) ...

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