QUBO formulations for NP-Hard spanning tree problems
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We introduce a novel Quadratic Unconstrained Binary Optimization (QUBO) formulation method for spanning tree problems. Instead of encoding the presence of edges in the tree individually, we opt to encode spanning trees as a permutation problem. We apply our method to four NP-hard spanning tree variants, namely the k-minimum spanning tree, degree-constrained minimum spanning tree, minimum leaf spanning tree, and maximum leaf spanning tree. Our main result is a formulation with 𝒪(|V|k) variables for the k-minimum spanning tree problem, beating related strategies that need 𝒪(|V|^2) variables.
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