Minsum k-sink problem on path networks

Benkoczi, Robert; Bhattacharya, Binay; Higashikawa, Yuya; Kameda, Tiko; Katoh, Naoki

doi:10.1016/j.tcs.2019.05.047

Cited by 11 publications

(22 citation statements)

References 23 publications

(46 reference statements)

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“…Formulae (6) and (7) were first shown by Kamiyama et al [38] while (8) and (9) were shown in [33,35]. Note that i L (x) (resp.…”

Section: K-facility Location In Pathsmentioning

confidence: 93%

“…On the other hand, the minisum facility location problems in dynamic flow networks have not been studied much except for the problem in path networks [6,7,33,35]. Paper [33] treated the minisum k-facility location problem in a dynamic flow path network with uniform edge capacity, and proposed an O(kn 2 ) time algorithm, which was improved to min{O(n 2 √ k log n + n 2 log n), n 2 2 O( √ log k log log n) } by the same authors in [35].…”

Section: Optimal Facility Location Problems In Dynamic Networkmentioning

confidence: 99%

“…Recently, Benkoczi et al [6] have developed an O(kn log 3 n) time algorithm, which is the best so far. In [6], the authors also treated the case with general edge capacities and proposed an O(kn 2 log 2 n) time algorithm, which was improved to O(kn log 4 n) by the same authors in [7].…”

Section: Optimal Facility Location Problems In Dynamic Networkmentioning

confidence: 99%

“…The minisum k-facility location problems in a dynamic flow path network with uniform edge capacity have been studied in [33,35]. Very recently, Benkoczi et al [7] have studied the problem for the case of general edge capacities. In this section, we mainly introduce the algorithms for the case of uniform edge capacity in [33,35] and mention the results for the case of general edge capacities in [7] because of space limitations.…”

Section: K-facility Location In Pathsmentioning

confidence: 99%

“…Very recently, Benkoczi et al [7] have studied the problem for the case of general edge capacities. In this section, we mainly introduce the algorithms for the case of uniform edge capacity in [33,35] and mention the results for the case of general edge capacities in [7] because of space limitations. Given a dynamic flow path network N = (P = (V, E), w, l, c, ) defined in Sect.…”

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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“…Formulae (6) and (7) were first shown by Kamiyama et al [38] while (8) and (9) were shown in [33,35]. Note that i L (x) (resp.…”

Section: K-facility Location In Pathsmentioning

confidence: 93%

Section: Optimal Facility Location Problems In Dynamic Networkmentioning

confidence: 99%

Section: Optimal Facility Location Problems In Dynamic Networkmentioning

confidence: 99%

Section: K-facility Location In Pathsmentioning

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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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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