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We consider the problem of embedding the Steiner points of a Steiner treewith given topology into the rectilinear plane. Thereby, the length of the pathbetween a distinguished terminal and each other terminal must not exceed givenlength restrictions. We want to minimize the total length of the tree.  The problem can be formulated as a linear program and therefore it issolvable in polynomial time. In this paper we analyze the structure of feasibleembeddings and give a combinatorial polynomial time algorithm for the problem.Our algorithm combines a dynamic programming approach and binary search andrelies on the total unimodularity of a matrix appearing in a sub-problem.

The rectilinear Steiner tree problem with given topology and length restrictions