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A Dynamic Graph Network is a graph in which each edge has an associatedtravel time and a capacity (width) that limits the number of items that cantravel in parallel along that edge. Each vertex in this dynamic graph networkbegins with the number of items that must be evacuated into designated sinkvertices. A $k$-sink evacuation protocol finds the location of $k$ sinks andassociated evacuation movement protocol that allows evacuating all the items toa sink in minimum time. The associated evacuation movement must impose aconfluent flow, i.e, all items passing through a particular vertex exit thatvertex using the same edge. In this paper we address the $k$-sink evacuationproblem on a dynamic path network. We provide solutions that run in $O(n \logn)$ time for $k=1$ and $O(k n \log^2 n)$ for $k >1$ and work for arbitrary edgecapacities.

Optimal Evacuation Flows on Dynamic Paths with General Edge Capacities