IWOCA 2016: Combinatorial Algorithms pp 122-134

# Minimax Regret 1-Median Problem in Dynamic Path Networks

• Yuya Higashikawa
• Siu-Wing Cheng
• Tsunehiko Kameda
• Naoki Katoh
• Shun Saburi
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 9843)

## Abstract

This paper considers the minimax regret 1-median problem in dynamic path networks. In our model, we are given a dynamic path network consisting of an undirected path with positive edge lengths, uniform positive edge capacity, and nonnegative vertex supplies. Here, each vertex supply is unknown but only an interval of supply is known. A particular assignment of supply to each vertex is called a scenario. Given a scenario s and a sink location x in a dynamic path network, let us consider the evacuation time to x of a unit supply given on a vertex by s. The cost of x under s is defined as the sum of evacuation times to x for all supplies given by s, and the median under s is defined as a sink location which minimizes this cost. The regret for x under s is defined as the cost of x under s minus the cost of the median under s. Then, the problem is to find a sink location such that the maximum regret for all possible scenarios is minimized. We propose an $$O(n^3)$$ time algorithm for the minimax regret 1-median problem in dynamic path networks with uniform capacity, where n is the number of vertices in the network.

## Keywords

Minimax regret Sink location Dynamic flow Evacuation planning

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© Springer International Publishing Switzerland 2016

## Authors and Affiliations

• Yuya Higashikawa
• 1
• 6
• Siu-Wing Cheng
• 2
• Tsunehiko Kameda
• 3
• Naoki Katoh
• 4
• 6
• Shun Saburi
• 5
1. 1.Department of Information and System EngineeringChuo UniversityTokyoJapan
2. 2.Department of Computer Science and EngineeringThe Hong Kong University of Science and TechnologyHong KongChina
3. 3.School of Computing ScienceSimon Fraser UniversityBurnabyCanada
4. 4.Department of InformaticsKwansei Gakuin UniversitySandaJapan
5. 5.Department of Architecture and Architectural EngineeringKyoto UniversityKyotoJapan
6. 6.CREST, Japan Science and Technology Agency (JST)KawaguchiJapan