Minimax Regret 1-Median Problem in Dynamic Path Networks

Higashikawa, Yuya; Cheng, Siu-Wing; Kameda, Tiko; Katoh, Naoki; Saburi, Shun

doi:10.1007/978-3-319-44543-4_10

Cited by 2 publications

(6 citation statements)

References 20 publications

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“…If F ≤ E holds, we have A < E by (30), which contradicts (24). Also, if G ≤ H holds, we have D < H by (31), which contradicts (27).…”

Section: Claim 1 For Integers P Satisfyingmentioning

confidence: 97%

“…If F ≤ E holds, we have A < E by (30), which contradicts (24). Also, if G ≤ H holds, we have D < H by (31), which contradicts (27). (26), (30) and (31), that is, A < G holds, which contradicts (25).…”

Section: Claim 1 For Integers P Satisfyingmentioning

confidence: 97%

“…Also, if G ≤ H holds, we have D < H by (31), which contradicts (27). (26), (30) and (31), that is, A < G holds, which contradicts (25). ◻ We first overview an O(kn 2 log n) time algorithm by [28] for the case of general edge capacities.…”

Section: Claim 1 For Integers P Satisfyingmentioning

confidence: 99%

“…On the other hand, the problems adopting the total cost criterion have not been studied much except for the case of the 1-facility location in path networks. For the minimax regret 1-facility location problem in a dynamic flow path network adopting the total cost criterion, Higashikawa et al [30,31] provided an O(n 3 ) time algorithm, and this result has been improved to O(n 2 log 2 n) recently by Bhattacharya et al [9].…”

Section: Minimax Regret Facility Location Problems In Dynamic Flow Nementioning

confidence: 99%

“…The minimax regret 1-facility location problem in a dynamic flow path network adopting the total cost criterion has been studied in [9,30,31]. As mentioned above, this study has also assumed that the edge capacity is uniform and a facility can be located at any point in the network.…”

Section: K-facility Location In Pathsmentioning

confidence: 99%

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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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“…If F ≤ E holds, we have A < E by (30), which contradicts (24). Also, if G ≤ H holds, we have D < H by (31), which contradicts (27).…”

Section: Claim 1 For Integers P Satisfyingmentioning

confidence: 97%

Section: Claim 1 For Integers P Satisfyingmentioning

confidence: 97%

Section: Claim 1 For Integers P Satisfyingmentioning

confidence: 99%

Section: Minimax Regret Facility Location Problems In Dynamic Flow Nementioning

confidence: 99%

Section: K-facility Location In Pathsmentioning

confidence: 99%

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A Survey on Facility Location Problems in Dynamic Flow Networks

Higashikawa

Katoh

2019

Rev Socionetwork Strat

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Minmax Regret 1-Sink Location Problems on Dynamic Flow Path Networks with Parametric Weights

Fujie

Higashikawa

Katoh

et al. 2020

Preprint

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This paper addresses the minmax regret 1-sink location problem on dynamic flow path networks with parametric weights. We are given a dynamic flow network consisting of an undirected path with positive edge lengths, positive edge capacities, and nonnegative vertex weights. A path can be considered as a road, an edge length as the distance along the road and a vertex weight as the number of people at the site. An edge capacity limits the number of people that can enter the edge per unit time. We consider the problem of locating a sink in the network, to which all the people evacuate from the vertices as quickly as possible. In our model, each weight is represented by a linear function in a common parameter t, and the decision maker who determines the location of a sink does not know the value of t. We formulate the sink location problem under such uncertainty as the minmax regret problem. Given t and a sink location x, the cost of x under t is the sum of arrival times at x for all the people determined by t. The regret for x under t is the gap between the cost of x under t and the optimal cost under t. The task of the problem is formulated as the one to find a sink location that minimizes the maximum regret over all t. For the problem, we propose an O(n 4 2 α(n) α(n) log n) time algorithm where n is the number of vertices in the network and α(•) is the inverse Ackermann function. Also for the special case in which every edge has the same capacity, we show that the complexity can be reduced to O(n 3 2 α(n) α(n) log n).

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Minimax Regret 1-Median Problem in Dynamic Path Networks

Cited by 2 publications

References 20 publications

A Survey on Facility Location Problems in Dynamic Flow Networks

A Survey on Facility Location Problems in Dynamic Flow Networks

Minmax Regret 1-Sink Location Problems on Dynamic Flow Path Networks with Parametric Weights

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