Abstract
AbstractNumerous works have been reported on the facility location problem to minimize or maximize various objective functions for the locations of one or more facilities on graphs. A general approach to these problems is algorithmic, but solutions are seldom found in an explicit manner. By restricting the object graph to grid graphs, this paper gives solutions in an explicit manner to the center problem and the median problem which are fundamental in facility location problems.Strictly speaking: (i) we derive the relationship between the center and median of general graphs G1 and G2 and the center and median of the product graph G1 x G2; then (ii) we find a multicenter and multimedian of the path graph Pn on n vertices and from the results, solve a kind of multicenter and multimedian problem for grid graphs; and (iii) we solve a distance minimization problem on grid graphs.
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