Statistical Mechanics of Steiner Trees

Statistical mechanics of steiner trees.

The minimum weight Steiner tree (MST) is an important combinatorial optimization problem over networks that has applications in a wide range of fields. Here we discuss a general technique to translate the imposed global connectivity constrain into many local ones that can be analyzed with cavity equation techniques. This approach leads to a new optimization algorithm for MST and allows us to an...

Statistical Alignment via k-Restricted Steiner Trees

When relating a set of sequences by a phylogeny, we are essentially constructing a Steiner tree connecting the sequences in the space of all finite sequences. Finding an optimal Steiner tree is in most formulations hard, so population genetics and phylogenetics have often used spanning trees as an approximation for computational expediency. In this assessment you will be asked to investigate an...

Steiner Trees and Steiner Forests

Pseudo-Gilbert-Steiner trees

The Gilbert network problem is a generalization of the Steiner minimal tree problem derived by adding flow-dependent weights to the edges. In this paper, we define a special class of minimum Gilbert networks, called pseudo-Gilbert–Steiner trees, and we show that it can be constructed by Gilbert’s generalization of Melzak’s method. Besides, a counterexample, a pseudo-Gilbert–Steiner tree, is con...

Preferred Direction Steiner Trees

The planar rectilinear Steiner tree problem has been extensively studied. The common formulation ignores circuit fabrication issues such as multiple routing layers, preferred routing directions, and vias between layers. In this paper, the authors extend a previously presented planar rectilinear Steiner tree heuristic to consider layer assignment, preferred routing direction restrictions, and vi...