On exact solutions for the rectilinear Steiner tree problem
SCG '97 Proceedings of the thirteenth annual symposium on Computational geometry
Computing optimal rectilinear Steiner trees: a survey and experimental evaluation
Discrete Applied Mathematics - Special volume on VLSI
Representing rectilinear Steiner trees in genetic algorithms
SAC '96 Proceedings of the 1996 ACM symposium on Applied Computing
A new heuristic for rectilinear Steiner trees
ICCAD '99 Proceedings of the 1999 IEEE/ACM international conference on Computer-aided design
Encoding rectilinear Steiner trees as lists of edges
Proceedings of the 2001 ACM symposium on Applied computing
Data Structures and Algorithms
Data Structures and Algorithms
Optimal Rectilinear Steiner Tree Routing in the Presence of Obstacles (supercedes CS-92-39, CS-93-15, and CS-93-19)
A scalable genetic algorithm for the rectilinear Steiner problem
CEC '02 Proceedings of the Evolutionary Computation on 2002. CEC '02. Proceedings of the 2002 Congress - Volume 02
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Given sets of points and obstacles in the plane, the rectilinear Steiner problem with obstacles seeks to connect the points with a rectilinear Steiner tree---a tree made up of vertical and horizontal line segments---that avoids the obstacles and has minimum total length. We consider only rectangular obstacles and further restrict the problem by requiring that it be possible to connect every point to the tree via exactly one vertical and one horizontal segment. Rectilinear Steiner trees that conform to this restriction can be represented by spanning trees augmented to specify the rectilinear segments. A genetic algorithm that uses a spanning-tree-based coding of rectilinear Steiner trees outperforms a greedy heuristic on 45 instances of the problem, of up to 469 points and 325 obstacles. However, the coding cannot represent arbitrary rectilinear Steiner trees, so it cannot address the unrestricted case, and in the case considered here, it leaves some potentially shorter trees unexamined.