On a generalization of a covering problem on undirected flow networks

Tamura, Hiroshi; Sugawara, Hidehito; Sengoku, Masakazu; Shoji, Shuichi

doi:10.1109/apcas.1996.569313

Cited by 8 publications

(11 citation statements)

References 3 publications

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“…Tamura et al [16][17][18][19] introduced the single source location problem and developped an O(nM (n, m)) algorithm where M (n, m) denotes the time complexity of computing a maximal flow. Initially, the algorithm was only applicable to uniform cost and uniform capacity instances but in the following papers they were able to transfer the algorithm to arbitrary cost and arbitrary capacity instances.…”

Section: Single Source Location Problemmentioning

confidence: 99%

“…Tamura et al [18,19] introduced the plural source location problem. 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.…”

Section: Plural Source Location Problemmentioning

confidence: 99%

“…Due to the equivalence of uncapacitated single source and single sink problems, we can conclude from Tamura et al [16][17][18][19]: W is an (uncapacitated) sink cover if and only if W ∩ X = ∅ for all minimal deficient sets X of G. W is feasible for the capacitated problem if and only if there exists some w ∈ W ∩ X such that k(W ) ≥ max x∈X a(x).…”

Section: Single Non-simultaneous Independentsink Location Problemmentioning

confidence: 99%

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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: Single Source Location Problemmentioning

confidence: 99%

Section: Plural Source Location Problemmentioning

confidence: 99%

Section: Single Non-simultaneous Independentsink Location Problemmentioning

confidence: 99%

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Sink location to find optimal shelters in evacuation planning

Heßler

Hamacher

2016

EURO Journal on Computational Optimization

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“…They also show that the (undirected) Source Location problem is NP-hard with arbitrary vertex costs. Polynomial time algorithms for several variants of SL with uniform vertex costs have been given [Bárász et al 2005;Nagamochi et al 2001;Tamura et al 1996;van den Heuvel and Johnson 2008]. Since the preliminary version of this paper, · 3 there has been much additional progress on many SL variants.…”

Section: Introductionmentioning

confidence: 99%

Simultaneous source location

Andreev

Garrod

Golovin

et al. 2009

ACM Trans. Algorithms

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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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“…In particular, if the capacities are sufficiently large, our problem represents the 1-center location problem. Secondly, our problem is an extension of the location problems based on flow (or connectivity) requirements in static networks, which have received much attention recently [1,10,16].…”

Section: Introductionmentioning

confidence: 99%

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

Mamada

Uno

Makino

et al.

IFIP International Federation for Information Processing

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In this paper, we consider a sink location in a dynamic network which consists of a graph with capacities and transit times on its arcs. Given a dynamic network with initial supplies at vertices, the problem is to find a vertex v as a sink in the network such that we can send all the initial supplies to v as quickly as possible.We present an O(n log 2 n) time algorithm for the sink location problem in a dynamic network of tree structure, where n is the number of vertices in the network. This improves upon the existing O(n 2 )-time bound. As a corollary, we also show that the quickest transshipment problem can be solved in O(n log 2 n) time if a given network is a tree and has a single sink. Our results are based on data structures for representing tables (i.e., sets of intervals with their height), which may be of independent interest.

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On a generalization of a covering problem on undirected flow networks

Cited by 8 publications

References 3 publications

Sink location to find optimal shelters in evacuation planning

Sink location to find optimal shelters in evacuation planning

Simultaneous source location

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

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