The Steiner tree problem, or the minimum Steiner tree problem, named after Jakob Steiner, is a problem in combinatorial optimization, which may be formulated in a number of settings, with the common part being that it is required to find the shortest interconnect for a given set of objects.

The Steiner tree problem is superficially similar to the minimum spanning tree problem: given a set V of points (vertices), interconnect them by a network (graph) of shortest length, where the length is the sum of the lengths of all edges. The difference between the Steiner tree problem and the minimum spanning tree problem is that, in the Steiner tree problem, extra intermediate vertices and edges may be added to the graph in order to reduce the length of the spanning tree. These new vertices introduced to decrease the total length of connection are known as Steiner points or Steiner vertices. It has been proved that the resulting connection is a tree, known as the Steiner tree. There may be several Steiner trees for a given set of initial vertices.

Kate Victoria "KT" Tunstall (born 23 June 1975, St Andrews, Fife, Scotland) is a Scottish singer-songwriter and guitarist. She broke into the public eye with a 2004 live solo performance of her song "Black Horse and the Cherry Tree" on Later... with Jools Holland. She has enjoyed commercial and critical success since, picking up three nominations before winning a BRIT Award, and a Grammy Award nomination. She is also the recipient of an Ivor Novello Award. Tunstall has a contralto vocal range.

She has released four albums internationally: Eye to the Telescope (2004), KT Tunstall's Acoustic Extravaganza (2006),Drastic Fantastic (2007) and Tiger Suit (2010). She has also done a guest appearance in an episode (S1E04) of the comedy series This is Jinsy on BBC Three.

Kate has a half-Chinese, half-Scottish mother and an Irish father. She was 18 days old when she was adopted by an English family in St Andrews, Scotland. Kate never got to meet her biological father. Her adoptive father was employed as a physics lecturer at the University of St Andrews, and her adoptive mother was a school teacher. Tunstall's family also includes an older brother named Joe and a younger brother named Daniel. Her parents had no interest in music and owned no records — the only tape her father owned was a comedy recording by mathematician and musical satirist Tom Lehrer.