Variant of the Steiner tree problem in geometry and combinatorics
The rectilinear Steiner tree problem, minimum rectilinear Steiner tree problem (MRST), or rectilinear Steiner minimum tree problem (RSMT) is a variant of the geometric Steiner tree problem in the plane, in which the Euclidean distance is replaced with the rectilinear distance. The problem may be formally stated as follows: given n points in the plane, it is required to interconnect them all by a shortest network which consists only of vertical and horizontal line segments. It can be shown that such a network is a tree whose vertices are the input points plus some extra points (Steiner points).[1]
The problem arises in the physical design of electronic design automation. In VLSI circuits, wire routing is carried out by wires running only in vertical and horizontal directions, due to high computational complexity of the task. Therefore wire length is the sum of the lengths of vertical and horizontal segments, and the distance between two pins of a net is actually the rectilinear distance ("Manhattan distance") between the corresponding geometric points in the design plane.[1]
^ abNaveed Sherwani, "Algorithms for VLSI Physical Design Automation"
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well-known variants are the Euclidean Steinertree problem and the rectilinear minimum Steinertree problem. The Steinertree problem in graphs can be seen as...
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2010-03-05. Garey, Michael R.; Johnson, David S. (1977). "The rectilinearSteinertree problem is NP-complete". SIAM Journal on Applied Mathematics. 32...
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