# Multiple Sink Location Problems in Dynamic Path Networks

• Yuya Higashikawa
• Mordecai J. Golin
• Naoki Katoh
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 8546)

## Abstract

This paper considers the k-sink location problem in dynamic path networks. In our model, a dynamic path network consists of an undirected path with positive edge lengths, uniform edge capacity, and positive vertex supplies. Here, each vertex supply corresponds to a set of evacuees. Then, the problem requires to find the optimal location of k sinks in a given path so that each evacuee is sent to one of k sinks. Let x denote a k-sink location. Under the optimal evacuation for a given x, there exists a (k − 1)-dimensional vector d, called (k − 1)-divider, such that each component represents the boundary dividing all evacuees between adjacent two sinks into two groups, i.e., all supplies in one group evacuate to the left sink and all supplies in the other group evacuate to the right sink. Therefore, the goal is to find x and d which minimize the maximum cost or the total cost, which are denoted by the minimax problem and the minisum problem, respectively. We study the k-sink location problem in dynamic path networks with continuous model, and prove that the minimax problem can be solved in O(kn logn) time and the minisum problem can be solved in O(kn 2) time, where n is the number of vertices in the given network.

## Keywords

sink location dynamic network evacuation planning

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© Springer International Publishing Switzerland 2014

## Authors and Affiliations

• Yuya Higashikawa
• 1
• Mordecai J. Golin
• 2
• Naoki Katoh
• 1
1. 1.Department of Architecture and Architectural EngineeringKyoto UniversityJapan
2. 2.Department of Computer Science and EngineeringThe Hong Kong University of Science and TechnologyHong Kong