# Preprocessing the Steiner Problem in Graphs

• Cees Duin
Chapter
Part of the Combinatorial Optimization book series (COOP, volume 6)

## Abstract

For combinatorial optimization problems that are NP-hard, it is important, before running a time consuming algorithm, to try to reduce the input size of the problem. This is the objective of a so-called preprocessing algorithm. A renowned NP-hard problem is the Steiner Problem in Graphs (SPG). It considers a weighted graph, denoted here as G = (V,K,E,c) with V the set of vertices, K a subset of so-called special vertices, E the set of undirected edges, and c: E→ Z + a positive integer weight function on E. The problem is to find a tree S of minimum total edge weight that spans the vertices of K.

## Keywords

Minimum Span Tree Steiner Tree Steiner Tree Problem Special Distance Special Vertex
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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