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Fixed-parameter algorithms for (k, r)-center in planar graphs and map graphs
2005
ACM Transactions on Algorithms
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:10.1145/1077464.1077468
fatcat:hfeciu7igncabltwzyokqs2fkm