In this paper, we consider a sink location in a dynamic network which consists of a graph with capacities and transit times on its arcs. Given a dynamic network with initial supplies at vertices, the problem is to find a vertex v as a sink in the network such that we can send all the initial supplies to v as quickly as possible.We present an O(n log 2 n) time algorithm for the sink location problem in a dynamic network of tree structure, where n is the number of vertices in the network. This improves upon the existing O(n 2 )-time bound. As a corollary, we also show that the quickest transshipment problem can be solved in O(n log 2 n) time if a given network is a tree and has a single sink. Our results are based on data structures for representing tables (i.e., sets of intervals with their height), which may be of independent interest.

In this paper, we present a first polynomial time algorithni for the monotone niin-max tree partitioning problem and show that the min-max tree partitioning problem is NP-hard if the eost function is not nmnotene. and that the min-sum tree partitioning problem is NP-hard even if the cost function is monotone.Wb also co}isider an evacuation problem in dynamic networks as an application of the tree partitio"ing problem. The evaeuation 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 tbe supplies going through a common vertex are sent out threugh a single are incident to it, since one of the ideal evacuation plans makes everyone to be evacuated fairly ancl without confusion.

No abstract

No abstract