Approaching the 5/4-Approximation for Rectilinear Steiner Trees
نویسندگان
چکیده
The rectilinear Steiner tree problem requires a shortest tree spanning a given vertex subset in the plane with rectilinear distance. It was proved that the output length of Zelikovsky's 25] and Berman/Ramaiyer 3] heuristics is at most 1.375 and 97 72 1:347 of the optimal length, respectively. It was claimed that these bounds are not tight. Here we improve these bounds to 1.3125 and 61 48 1:271, respectively, and give eecient algorithms to nd approximations of such quality. We also prove that for Zelikovsky's heuristic this bound cannot be less than 1.3.
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