Held–Karp algorithm
Algorithmic complexity

The Held–Karp algorithm has exponential time complexity Θ (2 n n 2) {\displaystyle \Theta (2^{n}n^{2})}, significantly better than the superexponential performance Θ (n !) {\displaystyle \Theta (n!)} of a brute-force algorithm. Held–Karp, however, requires Θ (n 2 n) {\displaystyle \Theta (n2^{n})} space to hold all computed values of the function g (S, e) {\displaystyle g(S,e)}, while brute force needs only Θ (n 2) {\displaystyle \Theta (n^{2})} space to store the graph itself.
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