Premium
An algorithm for the steiner problem in graphs
Author(s) -
Beasley J. E.
Publication year - 1984
Publication title -
networks
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.977
H-Index - 64
eISSN - 1097-0037
pISSN - 0028-3045
DOI - 10.1002/net.3230140112
Subject(s) - steiner tree problem , mathematics , combinatorics , undirected graph , maximum cut , connection (principal bundle) , graph , integer programming , reduction (mathematics) , discrete mathematics , algorithm , geometry
In this paper we consider the Steiner problem in graphs. This is the problem of connecting together, at minimum cost, a number of vertices in an undirected graph. We present two lower bounds for the problem, these bounds being based on two separate Lagrangian relaxations of a zero‐one integer programming formulation of the problem. Problem reduction tests derived from both the original problem and the Lagrangian relaxations are given. Incorporating the bounds and the reduction tests into a tree search procedure enables us to solve problems involving the connection of up to 50 vertices in a graph with 200 undirected arcs and 100 vertices.