Center location problems on tree graphs with subtree-shaped customers

Authors:
J. Puerto;A. Tamir;J. A. Mesa;D. Pérez-Brito
Affiliations:
Facultad de Matemáticas, Universidad de Sevilla, Spain;School of Mathematical Sciences, Tel Aviv University, Israel;ETS Ingenieros, Universidad de Sevilla, Spain;ETS Ingeniería Informática, Universidad de La Laguna, Spain
Venue:
Discrete Applied Mathematics
Year:
2008

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Abstract

We consider the p-center problem on tree graphs where the customers are modeled as continua subtrees. We address unweighted and weighted models as well as distances with and without addends. We prove that a relatively simple modification of Handler's classical linear time algorithms for unweighted 1- and 2-center problems with respect to point customers, linearly solves the unweighted 1- and 2-center problems with addends of the above subtree customer model. We also develop polynomial time algorithms for the p-center problems based on solving covering problems and searching over special domains.