Parameterized approximation of dominating set problems

Authors:
Rodney G. Downey;Michael R. Fellows;Catherine McCartin;Frances Rosamond
Affiliations:
Victoria University, Wellington, New Zealand;The University of Newcastle, Callaghan, Australia;Massey University, Palmerston North, New Zealand;The University of Newcastle, Callaghan, Australia
Venue:
Information Processing Letters
Year:
2008

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Abstract

A problem open for many years is whether there is an FPT algorithm that given a graph G and parameter k, either: (1) determines that G has no k-Dominating Set, or (2) produces a dominating set of size at most g(k), where g(k) is some fixed function of k. Such an outcome is termed an FPT approximation algorithm. We describe some results that begin to provide some answers. We show that there is no such FPT algorithm for g(k) of the form k+c (where c is a fixed constant, termed an additive FPT approximation), unless FPT=W[2]. We answer the analogous problem completely for the related Independent Dominating Set (IDS) problem, showing that IDS does not admit an FPT approximation algorithm, for any g(k), unless FPT=W[2].