Minimum-cost coverage of point sets by disks

We consider a class of geometric facility location problems in which the goal is to determine a set X of disks given by their centers (tj) and radii (rj) that cover a given set of demand points Y ⊂ R2 at the smallest possible cost. We consider cost functions of the form ∑j f (rj), where f (r) = rα is the cost of transmission to radius r. Special cases arise for α = 1 (sum of radii) and α = 2 (total area); power consumption models in wireless network design often use an exponent α > 2. Different scenarios arise according to possible restrictions on the transmission centers tj, which may be constrained to belong to a given discrete set or to lie on a line, etc. We obtain several new results, including (a) exact and approximation algorithms for selecting transmission points tj on a given line in order to cover demand points Y ⊂ R2; (b) approximation algorithms (and an algebraic intractability result) for selecting an optimal line on which to place transmission points to cove...

• Type: Conference
• Year: 2006
• Where: COMPGEOM
• Authors: Helmut Alt, Esther M. Arkin, Hervé Brönnimann, Jeff Erickson, Sándor P. Fekete, Christian Knauer, Jonathan Lenchner, Joseph S. B. Mitchell, Kim Whittlesey
• Keywords: COMPGEOM 2006, Demand Points, Smallest Possible Cost, Transmission Points