The Minimum Eccentricity Shortest Path Problem consists in finding a shortest path with minimum eccentricity in a given undirected graph. The problem is known to be NP-complete and W[2]-hard with respect to the desired eccentricity. We present fpt algorithms for the problem parameterized by the modular width, distance to cluster graph, the combination of distance to disjoint paths with the desired eccentricity, and maximum leaf number.

https://link.springer.com/chapter/10.1007/978-3-030-79987-8_31