An efficient parallel algorithm for the longest path problem in meshes
  In this paper, first we give a sequential linear-time algorithm for the longest path problem in meshes. This algorithm can be considered as an improvement of [13]. Then based on this sequential algorithm, we present a constant-time parallel algorithm for the problem which can be run on every parallel machine. 
Fatemeh Keshavarz-Kohjerdi and Alireza Bagheri
cs.DS