We present a new dynamic programming algorithm that solves minimum Steiner tree problems with k terminals in time O * (c k) for any c > 2. This improves the running time of the previously fastest exponential time algorithms (Dreyfus-Wagner [2]) of order O * (3 k) and the so-called "full set dynamic programming" algorithm, cf. [3], solving rectilinear instances in time O * (2.38 k).
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