set of intervals J is called a covering of P if each point in P is contained in at least one interval of Q. The Rainbow covering problem is the problem of finding a rainbow set Q that is a covering of P. The problem is NP-hard (by reduction from linear SAT). A more general notion is conflict-free covering. In this problem: There is a set O of m objects, and a conflict-graph GO on O. A subset Q of O is called conflict-free if it is an independent set in GO, that is, no two objects in Q are connected by an edge in GO. A rainbow set is a conflict-free set in the special case in which GO is made of disjoint cliques, where each clique represents a color. Conflict-free set cover is the problem of finding a conflict-free subset of O that is a covering of P. Banik, Panolan, Raman, Sahlot and Saurabh prove the following for the special case in which the conflict-graph has bounded arboricity: If the geometric cover problem is fixed-parameter tractable (FPT), then the conflict-free geometric cover problem is FPT. If the geometric cover problem admits an r-approximation algorithm, then the conflict-free geometric cover problem admits a similar approximation algorithm in FPT time. References