Minimax Regret 1-Sink Location Problems in Dynamic Path Networks

Cheng, Siu-Wing; Higashikawa, Yuya; Katoh, Naoki; Ni, Guanqun; Su, Bing; Xu, Yinfeng

doi:10.1007/978-3-642-38236-9_12

Cited by 22 publications

(33 citation statements)

References 14 publications

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“…Therefore, a function Θ i,j (x) is unimodal in x, and there exists the unique point which minimizes Θ i,j (x), they is, x * (1, i, j). Then, as [2,4,6] showed, we immediately have the following claim.…”

Section: Known Properties Of 1-sink Location Problemmentioning

confidence: 68%

Multiple Sink Location Problems in Dynamic Path Networks

Higashikawa

Golin

Katoh

2014

Algorithmic Aspects in Information and Management

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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) time and the minisum problem can be solved in O(n 2 · min{k, 2 √ log k log log n }) time, where n is the number of vertices in the given network. Note that these improve the previous results by [6].

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Section: Known Properties Of 1-sink Location Problemmentioning

confidence: 68%

Multiple Sink Location Problems in Dynamic Path Networks

Higashikawa

Golin

Katoh

2014

Algorithmic Aspects in Information and Management

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“…This formula was developed by [33,35] which has also been shown in [18,29]. Notice that this formula holds also for the case of general edge capacities.…”

Section: K-facility Location In Pathsmentioning

confidence: 82%

“…[Case 3]: By (18) and the condition of B < A , we have Also, by (19) and the condition of C < D , we have…”

Section: Claim 1 For Integers P Satisfyingmentioning

confidence: 99%

A Survey on Facility Location Problems in Dynamic Flow Networks

Higashikawa

Katoh

2019

Rev Socionetwork Strat

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This paper surveys the facility location problems in dynamic flow networks that have been actively studied in recent years. These problems have been motivated by evacuation planning which has become increasingly important in Japan. The evacuation planning problem is formulated using a dynamic flow network consisting of a graph in which a capacity as well as a transit time is associated with each edge. The goal of the problem is to find a way to send evacuees originally existing at vertices to facilities (evacuation centers) as quickly as possible. The problem can be viewed as a generalization of the classical k-center and k-median problems. In this paper we show recent results about the difficulty and approximability of a single facility location for general networks and polynomial time algorithms for k-facility location problems in path and tree networks. We also mention the minimax regret version of these problems. Fig. 2 A time-expanded network N(5) for the dynamic flow network N illustrated in Fig. 1. A number attached to a vertex represents its supply. A number attached to an edge represents its capacity buildings to reduce the loss of human lives from a tsunami triggered by the earthquake. In this respect, we hope that the methods developed for facility location problems will help to reduce the budget used for such disaster prevention and help reduce the loss of human lives.

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“…The minimax regret sink location problem was first proposed by Cheng et al (2013) in the context of the TohukuPacific Ocean Earthquake, which occurred in Japan on March 11, 2011. In general, the problem can be described as follows.…”

Section: Introductionmentioning

confidence: 99%

“…In this case, the evacuation time usually refers to the maximum time, i.e., the time required by the last unit weight to complete evacuation. Cheng et al (2013) considered the minimax regret 1-sink location problem in a dynamic path network with a uniform edge capacity, where an O n log 2 n time algorithm was proposed for the problem. Later, Wang (2014) and proposed two improved algorithms to address the problem, which each had a time complexity of O n log n .…”

Section: Introductionmentioning

confidence: 99%

Minimax regret 1-sink location problem with accessibility in dynamic general networks

2016

European Journal of Operational Research

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Minimax Regret 1-Sink Location Problems in Dynamic Path Networks

Cited by 22 publications

References 14 publications

Multiple Sink Location Problems in Dynamic Path Networks

Multiple Sink Location Problems in Dynamic Path Networks

A Survey on Facility Location Problems in Dynamic Flow Networks

Minimax regret 1-sink location problem with accessibility in dynamic general networks

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