An approximation scheme for finding Steiner trees with obstacles
SIAM Journal on Computing
Euclidean Steiner minimal trees with obstacles and Steiner visibility graphs
Discrete Applied Mathematics - Special issue on new frontiers in the theory and practice of combinatorial optimization: applications in manufacturing and VLSI design
LEDA: a platform for combinatorial and geometric computing
LEDA: a platform for combinatorial and geometric computing
Steiner Minimal Trees in Simple Polygons
Steiner Minimal Trees in Simple Polygons
Spanning trees in hypergraphs with applications to steiner trees
Spanning trees in hypergraphs with applications to steiner trees
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We consider the problem of determining a short Euclidean tree spanning a number of terminals in a simple polygon. First of all, linear time (in the number of vertices of the polygon) exact algorithms for this problem with three and four terminals are given. Next, these algorithms are used in a fast polynomial heuristic based on the concatenation of trees for appropriately selected subsets with up to four terminals. Computational results indicate that the solutions obtained are close to optimal solutions.