Minimum Eccentricity Shortest Path Problem: an Approximation Algorithm   and Relation with the k-Laminarity Problem
  The Minimum Eccentricity Shortest Path (MESP) Problem consists in determining a shortest path (a path whose length is the distance between its extremities) of minimum eccentricity in a graph. It was introduced by Dragan and Leitert [9] who described a linear-time algorithm which is an 8-approximation of the problem. In this paper, we study deeper the double-BFS procedure used in that algorithm and extend it to obtain a linear-time 3-approximation algorithm. We moreover study the link between the MESP problem and the notion of laminarity, introduced by V{\"o}lkel et al [12], corresponding to its restriction to a diameter (i.e. a shortest path of maximum length), and show tight bounds between MESP and laminarity parameters. 
Etienne Birmel\'e (MAP5), Fabien De Montgolfier (IRIF), L\'eo Planche   (MAP5, IRIF)
cs.CC cs.DM