Multiple sink location problems in dynamic path networks

Higashikawa, Yuya; Golin, Mordecai J.; Katoh, Naoki

doi:10.1016/j.tcs.2015.05.053

Cited by 27 publications

(75 citation statements)

References 5 publications

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“…Without loss of generality, we assume Φ s L (v 1 ) = 0 and Φ s R (v n ) = 0. We will show the formula of Φ s (x) that has been proved in [15,17]…”

Section: Total Evacuation Timementioning

confidence: 98%

“…, k}, we define σ i as σ i = ρi l=ρi−1+1 w s l , which is called the weight of i-th cluster. The interpretation can be derived from [15,17] as follows. The first unit on each v ρi does not encounter any congestion on its way to x.…”

Section: Total Evacuation Timementioning

confidence: 99%

“…We here show some properties on the 1-median problem in a dynamic path network N = (P = (V, E), l, w s , c, τ ) when a scenario s ∈ S is given, which were basically presented in [15,17]. We first introduce the following two lemmas.…”

Section: Known Properties For the Fixed Scenario Casementioning

confidence: 99%

“…In order to evaluate an evacuation, we can naturally consider two types of criteria: completion time criterion and total time criterion. In this paper we adopt the latter one (for the former one, refer to [12,15,17,18]). We here define a unit as an infinitesimally small portion of supply.…”

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confidence: 99%

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Minimax Regret 1-Median Problem in Dynamic Path Networks

Higashikawa

Cheng

Kameda

et al. 2016

Lecture Notes in Computer Science

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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.

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“…Without loss of generality, we assume Φ s L (v 1 ) = 0 and Φ s R (v n ) = 0. We will show the formula of Φ s (x) that has been proved in [15,17]…”

Section: Total Evacuation Timementioning

confidence: 98%

Section: Total Evacuation Timementioning

confidence: 99%

Section: Known Properties For the Fixed Scenario Casementioning

confidence: 99%

mentioning

confidence: 99%

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Minimax Regret 1-Median Problem in Dynamic Path Networks

Higashikawa

Cheng

Kameda

et al. 2016

Lecture Notes in Computer Science

Self Cite

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“…In a recent paper [15] on arXiv, the authors of [14] have improved the time complexities to O(max{k, log n} ⋅ kn log 4 n) and O(max{k, log n} ⋅ kn log 3 n) , respectively. Other than tree networks, Higashikawa et al [33] treated the minimax k-facility location problem in a dynamic flow path network with uniform edge capacity, and proposed an O(kn log n) time algorithm, which was improved to O(kn) by the same authors in [35]. Also, Higashikawa showed in his doctoral dissertation [28] that the minimax 1-facility and k-facility location problems in a dynamic flow path network with general edge capacities can be solved in O(n log n) time and O(kn 2 log n) time, respectively.…”

Section: Optimal Facility Location Problems In Dynamic Networkmentioning

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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Capacity provisioning for evacuation on path networks

Benkoczi

Lijoka

2022

Networks

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Designing an appropriate evacuation plan in the event of large scale disasters is extremely important. A considerable research effort has been invested in effective mathematical models and algorithms for the evacuation of densely populated areas. Dynamic networks and flows, and the closely related sink location and evacuation problems are research directions that are being actively pursued at the moment. In this work, we propose an extension of the sink location problem in dynamic networks that is suitable for planning the evacuation of remote and sparsely populated communities. We exploit the connection between the capacity of a transportation network and the amount of resources allocated to the rescue operation, and we introduce a new objective function for the problem of evacuation in a dynamic network. Given a network with known edge lengths and with a known number of evacuees located at the vertices, we would like to assign capacities to the edges of the network, from a fixed capacity budget, in such a way that the evacuation time of all evacuees to the set of fixed sink nodes in the network is minimized. We consider a simple path network with one fixed sink node and observe that the solution can be obtained numerically from a non‐linear program. However, by exploiting two useful properties of the optimal capacity allocation, we propose a combinatorial algorithm that returns a parametric solution, that is, a solution that depends on a single parameter, namely the capacity assigned to one edge of the path. Our algorithm runs in time Ofalse(nlogn+nlogfalse(cfalse/ξfalse)false)$$ O\left(n\log n+n\log \left(c/\xi \right)\right) $$ where c$$ c $$ is the budgeted capacity, ξ$$ \xi $$ is the precision to which the solution is computed, and n$$ n $$ is the number of vertices occupied by evacuees in an false(n+1false)$$ \left(n+1\right) $$‐vertex path. This work is the first to consider the capacity allocation problem in the context of sink location problems.

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Multiple sink location problems in dynamic path networks

Cited by 27 publications

References 5 publications

Minimax Regret 1-Median Problem in Dynamic Path Networks

Minimax Regret 1-Median Problem in Dynamic Path Networks

A Survey on Facility Location Problems in Dynamic Flow Networks

Capacity provisioning for evacuation on path networks

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