# Steiner problem

Find a subgraph of a graph, say $LaTeX: \textstyle G' = [V',E'],$ such that $LaTeX: V'$ contains $LaTeX: V^*$ (a specified subset of nodes), and $LaTeX: \textstyle \sum \{c(e): e \in E'\}$ is minimized. It is generally assumed $LaTeX: \textstyle c \ge 0.$ When $LaTeX: \textstyle |V^*|=2,$ this is the shortest path problem. When $LaTeX: \textstyle |V^*|=|V|,$ this is the (minimum) spanning tree problem.