A fast heuristic algorithm for the maximum concurrent k-splittable flow problem

Caramia, Massimiliano; Sgalambro, Antonino

doi:10.1007/s11590-009-0147-4

Cited by 13 publications

(8 citation statements)

References 29 publications

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“…We adopt the Randomized Rounding algorithm (RR) as a competing approach to our matheuristic on very large-size instances where optimal values are not available as a benchmark for quality solution. The RR algorithm was proposed by Raghavan and Tompson [34] and frequently employed to tackle large instances of static k-Splittable Flow Problems, see for example Bia loń [9] and Caramia and Sgalambro [33]. In the static framework the RR initially solves the relaxation of the path-restricted original problem where no limitation on the maximum number of paths is imposed, namely the free-flow relaxation.…”

Section: A Competing Approachmentioning

confidence: 99%

“…The strategies differ themselves on the type of relaxation applied to the original problem to obtain an initial solution satisfying the commodity demands. Caramia and Sgalambro [32,33] dealt with the Maximum Concurrent kSF P , where the aim is to maximize the routable demand fraction. They presented an exact algorithm based on Branch&Bound rules and a fast two stage heuristic algorithm.…”

Section: Introductionmentioning

confidence: 99%

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A matheuristic approach for the Quickest Multicommodity k-Splittable Flow Problem

Melchiori

Sgalambro

2018

Computers & Operations Research

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The literature on k-splittable flows, see Baier et al. (2002) [1], provides evidence on how controlling the number of used paths enables practical applications of flows optimization in many real-world contexts. Such a modeling feature has never been integrated so far in Quickest Flows, a class of optimization problems suitable to cope with situations such as emergency evacuations, transportation planning and telecommunication systems, where one aims to minimize the makespan, i.e. the overall time needed to complete all the operations, see Pascoal et al. (2006) [2]. In order to bridge this gap, a novel optimization problem, the Quickest Multicommodity k-Splittable Flow Problem (QM CkSF P) is introduced in this paper. The problem seeks to minimize the makespan of transshipment operations for given demands of multiple commodities, while imposing restrictions on the maximum number of paths for each single commodity. The computational complexity of this problem is analyzed, showing its N P-hardness in the strong sense, and an original Mixed-Integer Programming formulation is detailed. We propose a matheuristic algorithm based on a hybridized Very Large-Scale Neighborhood Search that, utilizing the presented mathematical formulation, explores multiple search spaces to solve efficiently large instances of the QM CkSF P. High quality computational results obtained on benchmark test sets are presented and discussed, showing how the proposed matheuristic largely outperforms a state-of-the-art heuristic scheme frequently adopted in path-restricted flow problems.

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Section: A Competing Approachmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

A matheuristic approach for the Quickest Multicommodity k-Splittable Flow Problem

Melchiori

Sgalambro

2018

Computers & Operations Research

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“…They are faster, they often deliver guarantees for the solving time but give only approximate solutions without a formal assessment of the quality (proximity). Caramia and Sgalambro [5] consider a maximum-flow model. They compute each path for a commodity and the related flows according to the polynomial scheme from [1].…”

Section: Related Workmentioning

confidence: 99%

A randomized rounding approach to a k-splittable multicommodity flow problem with lower path flow bounds affording solution quality guarantees

Białoń

2016

Telecommun Syst

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In 2005, Baier et al. introduced a "k-splittable" variant of the multicommodity flow (MCF) problem in which a given commodity was allowed to flow through a number of paths limited by a small integer. This problem enables a better use of the link capacities than the classical Kleinberg's unsplittable MCF problem while not overloading the used devices and protocols with a large number of paths. We solve a minimum-congestion k-splittable MCF problem coming from a practice of managing an software-defined, circuit switching network. We introduce a lower bound for a path flow in order to model a QoS demand for a single connection running the path. Instead of reducing the problem to the unsplittable flow problem, as suggested by Baier et al., we propose a potentially more exact method. We directly enhance the Raghavan and Thompson's randomized rounding for ordinary MCF problems to account for k-splittability and the lower flow bounds. A mechanism is constructed that prevents rounding up low flows in the subproblem solution to big values. It is based on modifying the continuous subproblem by additionally penalizing flows of certain commodities in certain links. When k = 1, this allows us to prove a property similar to the O( √ log m) approximation factor, where m denotes the number of network links. We give probabilistic guarantees for the solution quality and examine the behavior of the method experimentally.

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“…To our best knowledge, the ME k SF problem has not been studied. However, the maximum k -splittable flow (M k SF) problem, which is related to the ME k SF problem, has been extensively studied and has various applications in commodity transportation and telecommunication network optimization [13–18]. …”

Section: Introductionmentioning

confidence: 99%

A graph-based approach for proteoform identification and quantification using top-down homogeneous multiplexed tandem mass spectra

Zhu

Liu

2018

BMC Bioinformatics

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BackgroundTop-down homogeneous multiplexed tandem mass (HomMTM) spectra are generated from modified proteoforms of the same protein with different post-translational modification patterns. They are frequently observed in the analysis of ultramodified proteins, some proteoforms of which have similar molecular weights and cannot be well separated by liquid chromatography in mass spectrometry analysis.ResultsWe formulate the top-down HomMTM spectral identification problem as the minimum error k-splittable flow problem on graphs and propose a graph-based algorithm for the identification and quantification of proteoforms using top-down HomMTM spectra.ConclusionsExperiments on a top-down mass spectrometry data set of the histone H4 protein showed that the proposed method identified many proteoform pairs that better explain the query spectra than single proteoforms.Electronic supplementary materialThe online version of this article (10.1186/s12859-018-2273-4) contains supplementary material, which is available to authorized users.

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A fast heuristic algorithm for the maximum concurrent k-splittable flow problem

Cited by 13 publications

References 29 publications

A matheuristic approach for the Quickest Multicommodity k-Splittable Flow Problem

A matheuristic approach for the Quickest Multicommodity k-Splittable Flow Problem

A randomized rounding approach to a k-splittable multicommodity flow problem with lower path flow bounds affording solution quality guarantees

A graph-based approach for proteoform identification and quantification using top-down homogeneous multiplexed tandem mass spectra

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