The shortest multipaths problem in a capacitated dense channel

In this paper, we present a simple polynomial-time algorithm solving the shortest multipaths problem in particular grid graphs called dense channels. Our work extends the results of Formann et al. [M. Formann, D. Wagner, F. Wagner, Routing through a dense channel with minimum total wire length, Journal of Algorithms 15 (1993) 267–283], by considering arbitrary horizontal and vertical capacities.