A copy of this work was available on the public web and has been preserved in the Wayback Machine. The capture dates from 2006; you can also visit the original URL.
The file type is `application/pdf`

.

##
###
Fixed-Parameter Algorithms for the (k, r)-Center in Planar Graphs and Map Graphs
[chapter]

2003
*
Lecture Notes in Computer Science
*

The (k, r)-center problem asks whether an input graph G has ≤ k vertices (called centers) such that every vertex of G is within distance ≤ r from some center. In this article we prove that the (k, r)-center problem, parameterized by k and r, is fixed-parameter tractable (FPT) on planar graphs, i.e., it admits an algorithm of complexity f (k, r)n O(1) where the function f is independent of n. In particular, we show that f (k, r) = 2 O(r log r) √ k , where the exponent of the exponential term

doi:10.1007/3-540-45061-0_65
fatcat:k3gzdcsewrf4zmgg4mfro2fp2u