Almost Linear Time Algorithms for Some Problems on Dynamic Flow Networks

AbstractMotivated by evacuation planning, several problems regarding dynamic flow networks have been studied in recent years. A dynamic flow network consists of an undirected graph with positive edge lengths, positive edge capacities, and positive vertex weights. The road network in an area can be treated as a graph where the edge lengths are the distances along the roads and the vertex weights are the number of people at each site. An edge capacity limits the number of people that can enter the edge per unit time. In a dynamic flow network, when particular points on edges or vertices called sinks are given, all of the people are required to evacuate from the vertices to the sinks as quickly as possible. This chapter gives an overview of two of our recent results on the problem of locating multiple sinks in a dynamic flow path network such that the max/sum of evacuation times for all the people to sinks is minimized, and we focus on techniques that enable the problems to be solved in almost linear time.