The 1-center problem: Exploiting block structure

The 1-center problem: Exploiting block structure

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Article ID: iaor19881086
Country: United States
Volume: 22
Issue: 4
Start Page Number: 259
End Page Number: 269
Publication Date: Nov 1988
Journal: Transportation Science
Authors: , ,
Abstract:

A block of a graph is a maximal nonseparable subgraph. The authors show how the knowledge of block structure can be used to help solve the nonlinear 1-center problem on graphs which are more general than trees. They give an efficient algorithm which either finds a unique 1-center at some vertex, or else localizes the search for all 1-centers to a single block. The algorithm makes use of an associated graph, called a blocking graph, which is a tree, and iteratively orients arcs in the blocking graph to ‘point the way’ to a block which contains all 1-centers.

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