Polynomial kernels for tracking shortest paths

Václav Blazej, Pratibha Choudhary, Dusan Knop, Jan Matyás Kristan, Ondrej Suchý, Tomás Valla

Abstract: Highlights•A kernel with O(k2)$\mathcal{O}(k^2)$ edges for Tracking Paths in DAG, where k is the size of the solution.•A kernel with O(k)$\mathcal{O}(k)$ edges for Tracking Paths in DAG, when the input graph is planar.•For Tracking Shortest Paths, this implies a kernel with O(k4)$\mathcal{O}(k^4)$ edges in general graphs and O(k2)$\mathcal{O}(k^2)$ edges in planar graphs.•Single exponential algorithm for Tracking Shortest Paths in planar graphs.