IWOCA 2018: Combinatorial Algorithms pp 78-89

# Minsum k-Sink Problem on Dynamic Flow Path Networks

• Robert Benkoczi
• Binay Bhattacharya
• Yuya Higashikawa
• Tsunehiko Kameda
• Naoki Katoh
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 10979)

## Abstract

In emergencies such as earthquakes, nuclear accidents, etc., we need an evacuation plan. We model a street, a building corridor, etc. by a path network, and consider the problem of locating a set of k sinks on a dynamic flow path network with n vertices, where people are located, that minimizes the sum of the evacuation times of all evacuees. Our minsum model is more difficult to deal with than the minmax model, because the cost function is not monotone along the path. We present an $$O(kn^2\log ^2 n)$$ time algorithm for solving this problem, which is the first polynomial time result. If the edge capacities are uniform, we give an $$O(kn\log ^3 n)$$ time algorithm.

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© Springer International Publishing AG, part of Springer Nature 2018

## Authors and Affiliations

• Robert Benkoczi
• 1
• Binay Bhattacharya
• 2
• Yuya Higashikawa
• 3
• Tsunehiko Kameda
• 2
Email author
• Naoki Katoh
• 4
1. 1.Department of Mathematics and Computer ScienceUniversity of LethbridgeLethbridgeCanada
2. 2.School of Computing ScienceSimon Fraser UniversityBurnabyCanada