Center location problems on tree graphs with subtree-shaped customers (original) (raw)

We consider the p-center problem on tree graphs where the customers are modeled as continua subtrees. We address unweighted 4 and weighted models as well as distances with and without addends. We prove that a relatively simple modification of Handler's 5 classical linear time algorithms for unweighted 1-and 2-center problems with respect to point customers, linearly solves the 6 unweighted 1-and 2-center problems with addends of the above subtree customer model. We also develop polynomial time 7 algorithms for the p-center problems based on solving covering problems and searching over special domains.