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In combinatorial mathematics, the Steiner tree problem, or minimum Steiner tree problem, named after Jakob Steiner, is an umbrella term for a class of problems in combinatorial optimization. While Steiner tree problems may be formulated in a number of settings, they all require an optimal interconnect for a given set of objects and a predefined ...
A minimum single-trunk Steiner tree (MSTST) may be found in O(n log n) time. However simply finding all its edges requires linear time . The idea is that STSTs for a given point set essentially have only one "degree of freedom", which is the position of the horizontal trunk.
Example of rectilinear minimum spanning tree from random points. In graph theory, the rectilinear minimum spanning tree (RMST) of a set of n points in the plane (or more generally, in ) is a minimum spanning tree of that set, where the weight of the edge between each pair of points is the rectilinear distance between those two points.
A minimum-cost spanning-forest game (MCSF game) is a generalization of an MCST game, in which multiple supply-nodes are allowed. In general, the core of an MCSF game may be empty. [ 1 ] However, if the underlying network is a tree, the core is always non-empty, and core points can be computed in strongly-polynomial time .
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