A tree partitioning problem arising from an evacuation problem in tree dynamic networks

In this paper, we present a first polynomial time algorithm for the monotone min–max tree partitioning problem and show that the min–max tree partitioning problem is NP-hard if the cost function is not monotone, and that the min–sum tree partitioning problem is NP-hard even if the cost function is monotone. We also consider an evacuation problem in dynamic networks as an application of the tree partitioning problem. The evaucation problem is one of the basic studies on crisis management systems for evacuation guidance of residents against large-scale disasters. We restrict our attention to tree networks and consider flows such that all the supplies going through a common vertex are sent out through a single arc incident to it, since one of the ideal evacuation plans makes everyone to be evacuated fairly and without confusion.