Locating Sources to Meet Flow Demands in Undirected Networks

Arata, Kouji; Iwata, Satoru; Makino, Kazuhisa; Fujishige, Satoru

doi:10.1007/3-540-44985-x_27

Cited by 17 publications

(34 citation statements)

References 6 publications

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“…Their polynomial solution algorithms where later improved by Ito et al [22] and Arata et al [3] to a time complexity of O(nM (n, m)) for a greedy type algorithm and to O(n(m + n log n)) for an algorithm based on maximum adjacency orderings. However, these algorithms are only applicable to instances where the sources can be ordered in a specific way.…”

Section: Plural Source Location Problemmentioning

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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Section: Plural Source Location Problemmentioning

confidence: 99%

Sink location to find optimal shelters in evacuation planning

Heßler

Hamacher

2016

EURO Journal on Computational Optimization

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“…From this point of view, H. Ito et al considered the node to area connectivity (NA-connectivity, for short) as a concept that represents the connectivity between vertices and sets of vertices (areas) in a graph [9,10,12]. As related problems, the problem of locating a set W of vertices offering service with requirements measured by connectivity has been also studied [1,11,12,19].…”

Section: Introductionmentioning

confidence: 99%

Minimum Augmentation of Edge-Connectivity between Vertices and Sets of Vertices in Undirected Graphs

Ishii

Akiyama²,

Nagamochi

2008

Algorithmica

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Given an undirected multigraph G = (V, E), a family W of areas W ⊆ V , and a target connectivity k ≥ 1, we consider the problem of augmenting G by the smallest number of new edges so that the resulting graph has at least k edge-disjoint paths between v and W for every pair of a vertex v ∈ V and an area W ∈ W. So far this problem was shown to be NP-complete in the case of k = 1 and polynomially solvable in the case of k = 2. In this paper, we show that the problem for k ≥ 3 can be solved in O(m+n(k 3 +n 2 )(p+kn+n log n) log k+pkn 3 log (n/k)) time, where n = |V |, m = |{{u, v}|(u, v) ∈ E}|, and p = |W|. * An extended abstract of this paper was presented at 9th

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“…Arata et al [Arata et al 2002] gave an exact algorithm for the undirected SL with uniform vertex costs. They also show that the (undirected) Source Location problem is NP-hard with arbitrary vertex costs.…”

Section: Introductionmentioning

confidence: 99%

Simultaneous Source Location

Andreev¹,

Garrod²,

Maggs³

et al. 2004

Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques

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We consider the problem of Simultaneous Source Location -selecting locations for sources in a capacitated graph such that a given set of demands can be satisfied simultaneously, with the goal of minimizing the number of locations chosen. For general directed and undirected graphs we give an O(log D) approximation algorithm, where D is the sum of demands, and prove matching Ω(log D) hardness results assuming P = NP. For undirected trees, we give an exact algorithm and show how this can be combined with a result of Räcke to give a solution that exceeds edge capacities by at most O(log 2 n log log n), where n is the number of nodes. For undirected graphs of bounded treewidth we show that the problem is still NP-Hard, but we are able to give a PTAS with at most (1 + ) violation of the capacities for arbitrarily small , or a (k + 1)-approximation with exact capacities, where k is the treewidth.

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Locating Sources to Meet Flow Demands in Undirected Networks

Cited by 17 publications

References 6 publications

Sink location to find optimal shelters in evacuation planning

Sink location to find optimal shelters in evacuation planning

Minimum Augmentation of Edge-Connectivity between Vertices and Sets of Vertices in Undirected Graphs

Simultaneous Source Location

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