Optimal routing with failure‐independent path protection

Stidsen, Thomas Jacob Riis; Petersen, B.; Spoorendonk, Simon; Zachariasen, Martin; Rasmussen, Kasper

doi:10.1002/net.20323

Cited by 18 publications

(28 citation statements)

References 22 publications

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“…To overcome the noncompactness, column (path) generation can be used (see References [2,9]). However, it turns out that the related path generation (pricing) problems are difficult and have recently been proved to be NP-hard, see References [3][4][5][6] (a recent survey of path generation issues in resilient network design can be found in Reference [7]). NP-hardness of path generation for the LP version of our basic problem is demonstrated in Reference [6].…”

Section: Introductionmentioning

confidence: 99%

Complexity of resilient network optimisation

Żotkiewicz

Pióro²,

Tomaszewski

2009

Trans Emerging Tel Tech

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SUMMARYPath restoration (PR) is one of the basic mechanisms for securing telecommunication networks against failures. In the paper, we discuss the complexity of certain variants of a multi-commodity flow network optimisation problem in directed graphs related to state-independent path restoration mechanisms. We demonstrate that most variants of the considered problem are NP-hard. Depending on the variant, we show how the problem can be reduced either from the partition problem or from the problem of finding an arc-disjoint pair of paths that connect two distinct pairs of nodes. We also demonstrate that at the same time the considered problem is difficult to approximate. The complexity results of the paper are important as they can help to devise proper algorithms for resilient network design tools.

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Section: Introductionmentioning

confidence: 99%

Complexity of resilient network optimisation

Żotkiewicz

Pióro²,

Tomaszewski

2009

Trans Emerging Tel Tech

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“…A general label-setting SPPRC algorithm was used for the pricing problem related to another resilient design problem (state-independent restoration without stub-release) in [20]. However, as discussed in [6], it turns out that using general label-setting SPPRC algorithms for the pricing problems of PD and FR considered in this article is not effective either (as the MIP approach).…”

Section: Solution Through Path Generationmentioning

confidence: 93%

“…Still, according to computational experience described in [20] and [6], such a direct MIP approach is not efficient because the MIP model of the pricing problem does not solve well and fails to deliver solutions in a reasonable time already for networks of very moderate size (10 nodes, say).…”

Section: Solution Through Path Generationmentioning

confidence: 97%

“…However, it turns out that for most of the noncompact LP formulations of the optimization problems related to resilient network design, the corresponding path generation problems become apparently difficult, as observed for example in [19,23]. In fact, for several cases, the path generation problem has been proved to be N P-hard [4,8,12,16,17,20] (a survey on the path generation issues in resilient network design can be found in a recent report [18]). …”

Section: Introductionmentioning

confidence: 97%

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On the complexity of resilient network design

Tomaszewski

Pióro

Żotkiewicz³

2009

Networks

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In this article we prove N P-hardness of two well-known optimization problems related to the design of multicommodity flow networks with two different methods for providing network resiliency against failures: path diversity and flow restoration. Path diversity is a static mechanism that consists of using, for each demand, a number of paths and oversizing the flows assigned to these paths so that for any failure the total surviving flow is not less than the volume of the demand. By contrast, flow restoration is a dynamic mechanism that consists of reassigning the failed flows to backup paths when a failure occurs. Both mechanisms are of practical interest because although flow restoration is in general superior to path diversity in terms of the required amount of resource capacity, it might be too complicated to implement. By providing an appropriate reduction from the fractional graph coloring problem, we show that both problems are N P-hard in the general case of failure scenarios that admit simultaneous failures of multiple links. Finally, we discuss how to efficiently solve the two problems using path generation techniques.

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“…For each demand k, the pricing problem that has to be solved consists in finding a path with minimum reduced cost. The reduced cost of protection path p for demand k can be written as: (19) and (20) In Stidsen et al (2007), the joint optimization of working routing and SBPP in directed networks with asymmetric traffic is considered. The authors present an LP model solved by column generation.…”

Section: Shared Path Protection Modelmentioning

confidence: 99%

A unified framework for shared protection schemes in optical mesh network

Rocha

Jaumard

2009

Pesqui. Oper.

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While the advantages of p-cycles and FIPP p-cycles are well established, there has been no systematic analysis of how much bandwidth they consume in comparison with the classical shared link and path protection schemes. It was recently observed that, even enumerating a huge number of cycles, is not necessarily a guarantee for obtaining good quality solutions with the ILP models if tools for large scale programming are not used. We propose to investigate the bandwidth protection costs of p-cycles and FIPP p-cycles in comparison with those of shared link and path protection by applying the column generation technique to solve relaxed LP models for the four protection schemes, and then solving the resulting ILP models. Provably near-optimal solutions allow us to perform accurate quantitative comparisons on real-world networks.Keywords: optical networks; shared protection; column generation. ResumoEmbora as vantagens dos p-ciclos e FIPP p-ciclos estejam bem estabelecidas, não existe uma análise sistemática de quanta largura de banda eles consomem em comparação aos mecanismos clássicos de proteção compartilhada por caminhos e por links. Foi observado recentemente que a enumeração de um enorme número de ciclos não é necessariamente uma garantia de se obter soluções de boa qualidade se ferramentas para programação de larga escala não forem usadas. Nós propomos investigar os custos de proteção de largura de banda dos p-ciclos e FIPP p-ciclos em comparação com aqueles de proteção compartilhada por links e por caminhos, através da aplicação da técnica de geração de colunas para resolver modelos relaxados para os quatro esquemas de proteção. Em seguida, resolvemos os modelos de programação inteira resultantes. Soluções próximas da otimalidade nos permitem desempenhar comparações quantitativas exatas em redes reais.Palavras-chave: redes óticas; proteção compartilhada; geração de colunas.

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Optimal routing with failure‐independent path protection

Cited by 18 publications

References 22 publications

Complexity of resilient network optimisation

Complexity of resilient network optimisation

On the complexity of resilient network design

A unified framework for shared protection schemes in optical mesh network

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