Article ID: | iaor19982961 |
Country: | United States |
Volume: | 29 |
Issue: | 4 |
Start Page Number: | 255 |
End Page Number: | 263 |
Publication Date: | Apr 1997 |
Journal: | IIE Transactions |
Authors: | Palekar Udatta S., Chhajed Dilip |
Keywords: | graphs |
Given a set of points on a Cartesian plane and the coordinate axes, the rectilinear network design problem is to find a network, with arcs parallel to either one of the axes, that minimizes the fixed and the variable costs of interactions between a specified set of pairs of points. We show that, even in the presence of arbitrary barriers, an optimal solution to the problem (when feasible) is contained in a grid graph defined by the set of given points and the barriers. This converts the spatial problem to a combinatorial problem. Finally we show connections between the rectilinear network design problem and a number of well-known problems. Thus this paper unifies the known dominating set results for these problems and extends the results to the case with barriers.