Computing earliest arrival flows with multiple sources

Abstract

Earliest arrival flows are motivated by applications related to
  evacuation.  Given a network with capacities and transit times on
  the arcs, a subset of source nodes with supplies and a sink node,
  the task is to send the given supplies from the sources to the sink
  "as quickly as possible".  The latter requirement is made more
  precise by the earliest arrival property which requires that the
  total amount of flow that has arrived at the sink is maximal for all
  points in time simultaneously.

  It is a classical result from the 1970s that, for the special case
  of a single source node, earliest arrival flows do exist and can be
  computed by essentially applying the Successive Shortest Path
  Algorithm for min-cost flow computations.  While it has previously
  been observed that an earliest arrival flow still exists for
  multiple sources, the problem of computing one efficiently has been
  open.  We present an exact algorithm for this problem whose running
  time is strongly polynomial in the input plus output size of the
  problem.