Parameterized algorithms for locating-dominating sets

A locating-dominating set D of a graph G is dominating where each vertex not in has unique neighborhood D, and the Locating-Dominating Set problem asks if contains such bounded size. This known to be NP-hard even on restricted classes, as interval graphs, split planar bipartite subcubic graphs. On other hand, it solvable polynomial time for some trees and, more generally, graphs cliquewidth. While these results have numerous implications parameterized complexity problem, little terms kernelization under structural parameterizations. In this work, we begin filling gap literature. Our first result shows that W[1]-hard when by size minimum clique cover. We present an exponential kernel distance cluster parameterization show that, unless NP ? coNP/poly, no exists cover nor clique. then turn our attention parameters either previous two, exhibit linear parameterizing max leaf number; context, leave feedback edge primary open study.