Computing representative networks for braided rivers

Abstract

Drainage networks on terrains have been studied extensively from an algorithmic perspective. However, in drainage networks water flow cannot bifurcate and hence they do not model \emph{braided rivers} (multiple channels which split and join, separated by sediment bars). We initiate the algorithmic study of braided rivers by employing the descending quasi Morse-Smale complex on the river bed (a polyhedral terrain), and extending it with a certain ordering of bars from one river bank to the other. This allows us to compute a graph that models a representative channel network, consisting of lowest paths. To ensure that channels in this network are sufficiently different we define a \emph{sand function} that represents the volume of sediment separating them. We show that in general the problem of computing a maximum network of non-crossing channels which are $\delta$-different from each other (as measured by the sand function) is NP-hard. However, using our ordering between the river banks, we can compute a maximum $\delta$-different network that respects this order in polynomial time. We implemented our approach and applied it to simulated and real-world braided rivers.