Preprocessing the Steiner Problem in Graphs
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.
KeywordsMinimum Span Tree Steiner Tree Steiner Tree Problem Special Distance Special Vertex
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