Steiner Trees with Other Cost Functions and Constraints

Abstract

In this chapter we look at Steiner tree problems that involve other cost functions and constraints (beyond those discussed in the first three chapters) but that still can be solved exactly by exploiting the geometric properties of minimal solutions. We focus particularly on four types of Steiner tree problems: the gradient-constrained Steiner tree problem, which serves as another example of an exactly solvable Steiner tree problem in a Minkowski plane with useful applications; the obstacle-avoiding Steiner tree problem, which is an important variation of the Steiner tree problem with applications in the physical design of microchips; bottleneck and other k-Steiner tree problems, where there is a given bound on the number of Steiner points; and Steiner tree problems optimising a cost associated with flow on the network.