A Dynamic location problem for graphs

Abstract

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.

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Chung, F.R.K., Graham, R.L. & Saks, M.E. A Dynamic location problem for graphs. Combinatorica 9, 111–131 (1989). https://doi.org/10.1007/BF02124674

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