An O(n log2 n) Algorithm for a Sink Location Problem in Dynamic Tree Networks

Mamada, Satoko; Uno, Takeaki; Makino, Kazuhisa; Fujishige, Satoru

doi:10.1007/1-4020-8141-3_21

Cited by 26 publications

(48 citation statements)

References 12 publications

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“…If the height of an arriving section at vertex v i is higher than c i−1 , the evacuees carried by that section cannot depart from v i at the arrival rate. We see that the duration of the section gets stretched in this case, by the ceiling operation [23]. From now on, we use the verb ceil to mean performing a ceiling operation.…”

Section: Cluster/section Sequencementioning

confidence: 99%

“…Mamada et al [23] solved the minmax 1-sink problem for tree networks in O(n log 2 n) time under the condition that only a vertex can be a sink. When edge capacities are uniform, Higashikawa et al [18] and Bhattacharya and Kameda [7] presented O(n log n) time algorithms with a more relaxed condition that the sink can be on an edge.…”

Section: Introductionmentioning

confidence: 99%

“…Bhattacharya et al [5] recently improved these results to O(min{n log n, n + k 2 log 2 n) time in the uniform edge capacity case, and to O(min{n log 3 n, n log n + k 2 log 4 n}) time in the general case. [19], O(n + k 2 log 2 n) [5], O(n log n) [5] k-sink [G] O(n log n + k 2 log 4 n) [5], O(n log 3 n) [ [22] k-sink [U] O(kn 2 log 4 n) [9], O(max{k, log n}kn log 3 n) [8] k-sink [G] O(kn 2 log 5 n) [9], O(max{k, log n}kn log 4 n) [ The minsum objective function for the sink problems is motivated, among others, by the desire to minimize the transportation cost of evacuation or the total amount of psychological duress suffered by the evacuees. It is more difficult than the minmax variety because the objective cost function is not unimodal along a path, and, to the best of our knowledge, practically nothing is known about this problem on more general networks than path networks.…”

Section: Introductionmentioning

confidence: 99%

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Minsum k-sink problem on path networks

Benkoczi

Bhattacharya

Higashikawa

et al. 2020

Theoretical Computer Science

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We consider the problem of locating a set of k sinks on a path network with general edge capacities that minimizes the sum of the evacuation times of all evacuees. We first present an O(kn log 4 n) time algorithm when the edge capacities are non-uniform, where n is the number of vertices. We then present an O(kn log 3 n) time algorithm when the edge capacities are uniform. We also present an O(n log n) time algorithm for the special case where k = 1 and the edge capacities are non-uniform.

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Section: Cluster/section Sequencementioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Minsum k-sink problem on path networks

Benkoczi

Bhattacharya

Higashikawa

et al. 2020

Theoretical Computer Science

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“…Mamanda et al [30] give a faster algorithm for tree networks. Hall et al [20] study the case called uniform path-lengths where only a single sink t exists and for any vertex v all paths from v to s have the same transit time.…”

Section: Introduction and Related Workmentioning

confidence: 99%

Fast and Memory-Efficient Algorithms for Evacuation Problems

Schlöter¹,

Skutella²

2017

Proceedings of the Twenty-Eighth Annual ACM-SIAM Symposium on Discrete Algorithms

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We study two classical flow over time problems that capture the essence of evacuation planning. Given a network with capacities and transit times on the arcs and sources/sinks with supplies/demands, a quickest transshipment sends the supplies from the sources to meet the demands at the sinks as quickly as possible. In a 1995 landmark paper, Hoppe and Tardos describe the first strongly polynomial time algorithm solving the quickest transshipment problem. Their algorithm relies on repeatedly calling an oracle for parametric submodular function minimization.We present a somewhat simpler and more efficient algorithm for the quickest transshipment problem. Our algorithm (i) relies on only one parametric submodular function minimization and, as a consequence, has considerably improved running time, (ii) uses not only the solution of a submodular function minimization but actually exploits the underlying algorithmic approach to determine a quickest transshipment as a convex combination of simple lex-max flows over time, and (iii) in this way determines a structurally easier solution in the form of a generalized temporally repeated flow.Our second main result is an entirely novel algorithm for computing earliest arrival transshipments, which feature a particularly desirable property in the context of evacuation planning. An earliest arrival transshipment -which in general only exists in networks with a single sink -is a quickest transshipment maximizing the amount of flow which has reached the sink for every point in time simultaneously. In contrast to previous approaches, our algorithm solely works on the given network and, as a consequence, requires only polynomial space.

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“…There are, however, two papers which deal with similar problems. The first one is by Mamada et al [11]. Their problem is to find a single sink in a tree such that the supply of all nodes can be discharged to the sink as fast as possible.…”

Section: Introductionmentioning

confidence: 99%

Sink location to find optimal shelters in evacuation planning

Heßler

Hamacher

2016

EURO Journal on Computational Optimization

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The sink location problem is a combination of network flow and location problems: From a given set of nodes in a flow network a minimum cost subset W has to be selected such that given supplies can be transported to the nodes in W . In contrast to its counterpart, the source location problem which has already been studied in the literature, sinks have, in general, a limited capacity. Sink location has a decisive application in evacuation planning, where the supplies correspond to the number of evacuees and the sinks to emergency shelters.We classify sink location problems according to capacities on shelter nodes, simultaneous or non-simultaneous flows, and single or multiple assignments of evacuee groups to shelters. Resulting combinations are interpreted in the evacuation context and analyzed with respect to their worst-case complexity status.There are several approaches to tackle these problems: Generic solution methods for uncapacitated problems are based on source location and modifications of the network. In the capacitated case, for which source location cannot be applied, we suggest alternative approaches which work in the original network. It turns out that latter class algorithms are superior to the former ones. This is established in numerical tests including random data as well as real world data from the city of Kaiserslautern, Germany.

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An O(n log2 n) Algorithm for a Sink Location Problem in Dynamic Tree Networks

Cited by 26 publications

References 12 publications

Minsum k-sink problem on path networks

Minsum k-sink problem on path networks

Fast and Memory-Efficient Algorithms for Evacuation Problems

Sink location to find optimal shelters in evacuation planning

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