, Volume 9, Issue 2, pp 111-131

A Dynamic location problem for graphs

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We introduce a class of optimization problems, calleddynamic location problems, involving the processing of requests that occur sequentially at the nodes of a graphG. This leads to the definition of a new parameter of graphs, called the window indexWX(G), that measures how large a “window” into the future is needed to solve every instance of the dynamic location problem onG optimally on-line. We completely characterize this parameter:WX(G)≦k if and only ifG is a weak retract of a product of complete graphs of size at mostk. As a byproduct, we obtain two (polynomially recognizable) structural characterizations of such graphs, extending a result of Bandelt.