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There are many algorithms that find approximations of rectilinear Steiner minimum trees (RSMT). Among them are:

  • a suite of algorithms that find minimum spanning trees
  • RST-T (rectilinear single trunk Steiner tree)
  • BGA (batcheed greedy algorithm)
  • BI1S (Batched Iterated 1-Steiner tree)
  • FLUTE (Fast Lookup Table Based Technique for RSMT Construction and Wirelength Estimation)

It was showed that length of RSMT can be as much as 3/2 times that of rectlinear spanning minimum tree. I didn't find in literature bounds for other algorithms. Do they exist?

FLUTE seems to be the most efficient algorithm from all but I don't know it's worst case and upper bound. Was it found?

Does any algorithm have bound less than 3/2?

Andrei Botalov
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1 Answers1

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Arora and Mitchell gave polynomial-time approximation schemes (= for all epsilon > 0, a (1 + epsilon)-approximation) for Euclidean Steiner tree. I believe the ideas can be adapted straightforwardly to the rectilinear variant.

Per
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