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arxiv: 1906.10265 · v1 · pith:KYMQCBQ6new · submitted 2019-06-24 · 💻 cs.NI

Reliable Slicing of 5G Transport Networks with Dedicated Protection

Nashid Shahriar , Sepehr Taeb , Shihabur Rahman Chowdhury , Mubeen Zulfiqar , Massimo Tornatore , Raouf Boutaba , Jeebak Mitra , Mahdi Hemmati This is my paper

Pith reviewed 2026-05-25 16:35 UTC · model grok-4.3

classification 💻 cs.NI
keywords 5G transport slicingelastic optical networksdedicated protectionbandwidth squeezingmulti-path provisioningspectrum savingsnetwork reliability
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The pith

Elastic optical networks with bandwidth squeezing and multi-path provisioning use less spectrum for dedicated protection in 5G transport slices than fixed-grid networks.

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

This paper seeks to establish that 5G transport network slices can be made reliable with dedicated protection while using fewer spectrum resources by leveraging elastic optical networks. The approach combines bandwidth squeezing to provide less protection bandwidth and survivable multi-path provisioning to spread the load. EON features allow precise spectrum allocation by adapting modulation and error correction. Evaluations on realistic network topologies show these methods yield spectrum savings over traditional fixed-grid setups and reveal how squeezing and multi-path affect overall utilization.

Core claim

Dedicated protection for 5G transport slices in elastic optical networks, when combined with bandwidth squeezing and multi-path provisioning, achieves spectrum savings compared to fixed-grid optical networks by allowing flexible and rightsized resource allocation through fine-tuned spectrum, modulation, and FEC.

What carries the argument

Integration of EON flexible spectrum allocation with bandwidth squeezing and survivable multi-path provisioning to minimize backup resources for dedicated protection in virtual network slices.

Load-bearing premise

EON capabilities for fine-tuning spectrum allocation and adapting modulation format and FEC can be leveraged in practice without significant additional complexity or cost.

What would settle it

Re-running the numerical evaluation on the same realistic topologies but disabling EON adaptations or removing bandwidth squeezing and multi-path provisioning to check if spectrum savings vanish.

Figures

Figures reproduced from arXiv: 1906.10265 by Jeebak Mitra, Mahdi Hemmati, Massimo Tornatore, Mubeen Zulfiqar, Nashid Shahriar, Raouf Boutaba, Sepehr Taeb, Shihabur Rahman Chowdhury.

Figure 1
Figure 1. Figure 1: Benefits of virtual link demand splitting and the impact of availability of disjoint paths [PITH_FULL_IMAGE:figures/full_fig_p002_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: Impact of varying BSR on performance metrics in small Germany SN [PITH_FULL_IMAGE:figures/full_fig_p008_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: Analysis of our reliability model shows that SSUs decrease with increasing SN LNR even for the no protection case (0% BSR). This stems from the fact that an SN with a larger LNR reduces the lengths and the number of intermediate hops of the SPaths between the same pair of SNodes, thus facilitating the use of more spectrum efficient transmission configurations along fewer hops. However, the gain in spectrum… view at source ↗
Figure 5
Figure 5. Figure 5: Creating VLink ordering o ∗ 1 from o ∗ Lemma 1. The commonality index of VLink ordering o ∗ 1 is less than or equal to the commonality index of the VLink ordering o ∗ (w o ∗ 1 ≤ w o ∗ ). Proof. We divide the proof of the lemma in two parts. At first, we prove i) the effective commonality of all the VLinks (except e¯ o ∗ j ) in VLink ordering o ∗ 1 is less than or equal to the effective commonality of the s… view at source ↗
Figure 6
Figure 6. Figure 6: Dividing the VLinks into 3 groups to check their commonality indexes [PITH_FULL_IMAGE:figures/full_fig_p010_6.png] view at source ↗
read the original abstract

In 5G networks, slicing allows partitioning of network resources to meet stringent end-to-end service requirements across multiple network segments, from access to transport. These requirements are shaping technical evolution in each of these segments. In particular, the transport segment is currently evolving in the direction of the so-called elastic optical networks (EONs), a new generation of optical networks supporting a flexible optical-spectrum grid and novel elastic transponder capabilities. In this paper, we focus on the reliability of 5G transport-network slices in EON. Specifically, we consider the problem of slicing 5G transport networks, i.e., establishing virtual networks on 5G transport, while providing dedicated protection. As dedicated protection requires large amount of backup resources, our proposed solution incorporates two techniques to reduce backup resources: (i) bandwidth squeezing, i.e., providing a reduced protection bandwidth with respect to the original request; and (ii) survivable multi-path provisioning. We leverage the capability of EONs to fine tune spectrum allocation and adapt modulation format and Forward Error Correction (FEC) for allocating rightsize spectrum resources to network slices. Our numerical evaluation over realistic case-study network topologies quantifies the spectrum savings achieved by employing EON over traditional fixed-grid optical networks, and provides new insights on the impact of bandwidth squeezing and multi-path provisioning on spectrum utilization.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Referee Report

2 major / 1 minor

Summary. The paper proposes a dedicated-protection approach for reliable 5G transport-network slicing in elastic optical networks (EONs). It incorporates bandwidth squeezing (reduced protection bandwidth) and survivable multi-path provisioning to lower backup-resource consumption, while exploiting EON flexibility in spectrum allocation, modulation format, and FEC to right-size resources per slice. The central claim is that numerical evaluation on realistic topologies demonstrates spectrum savings relative to fixed-grid networks and yields new insights on the effects of squeezing and multi-path provisioning.

Significance. If the quantitative results hold after addressing modeling assumptions, the work supplies concrete evidence on how EON capabilities can reduce the resource penalty of dedicated protection in sliced 5G transport, together with practical insights on squeezing and multi-path. Such data would be useful for dimensioning reliable slices in next-generation optical backbones.

major comments (2)
  1. [Abstract] Abstract / Numerical evaluation: the reported spectrum savings rest on the untested premise that EON fine-grained allocation, adaptive modulation, and FEC incur no material overhead (guard bands, transponder cost, control-plane complexity, or extra FEC bits) compared with fixed-grid. The evaluation description models only the allocation benefit; if these offsets are non-negligible the claimed savings could shrink or reverse. This assumption is load-bearing for the central claim.
  2. [Abstract] Abstract: the numerical evaluation is described only at the level of 'realistic case-study network topologies' with no equations, traffic model, exclusion rules, or error bars supplied. Without these details the quantified savings cannot be reproduced or stress-tested, undermining verification of the main result.
minor comments (1)
  1. The abstract states that EON 'fine tune[s] spectrum allocation' but does not clarify whether the model includes the minimum slot granularity or guard-band requirements that are standard in EON literature.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for the constructive feedback on our manuscript. We address each major comment below, clarifying the scope of our model and offering revisions to improve transparency and reproducibility.

read point-by-point responses

  1. Referee: [Abstract] Abstract / Numerical evaluation: the reported spectrum savings rest on the untested premise that EON fine-grained allocation, adaptive modulation, and FEC incur no material overhead (guard bands, transponder cost, control-plane complexity, or extra FEC bits) compared with fixed-grid. The evaluation description models only the allocation benefit; if these offsets are non-negligible the claimed savings could shrink or reverse. This assumption is load-bearing for the central claim.

    Authors: We acknowledge that the evaluation focuses on spectrum allocation benefits from EON flexibility (fine-grained grid, adaptive modulation, and FEC) without explicitly modeling overheads such as guard bands, transponder costs, or control-plane complexity. Our optimization model abstracts to the core resource allocation problem under dedicated protection, bandwidth squeezing, and survivable multi-path routing. These overheads are implementation-specific and typically small relative to the modeled savings, but we agree the assumption should be stated explicitly. We will revise the manuscript to add a dedicated paragraph in the numerical evaluation section noting that reported savings represent an upper bound under idealized EON conditions and briefly discuss potential offsets with references to related EON literature. revision: yes

  2. Referee: [Abstract] Abstract: the numerical evaluation is described only at the level of 'realistic case-study network topologies' with no equations, traffic model, exclusion rules, or error bars supplied. Without these details the quantified savings cannot be reproduced or stress-tested, undermining verification of the main result.

    Authors: The abstract is kept concise per journal conventions. The full manuscript details the ILP formulation and equations in Section III, the traffic model (including slice requests and protection requirements) and specific realistic topologies in Section IV, path selection and exclusion rules within the survivable multi-path model, and all simulation parameters. Results are from deterministic optimization, so statistical error bars do not apply; we will ensure the evaluation section explicitly cross-references these elements for reproducibility and consider adding a brief sensitivity discussion if space allows. revision: partial

Circularity Check

0 steps flagged

No significant circularity; evaluation uses external topologies and independent modeling

full rationale

The paper proposes a solution for 5G transport slicing with dedicated protection in EONs, using bandwidth squeezing and multi-path provisioning to reduce backup resources, then evaluates spectrum savings versus fixed-grid networks on realistic case-study topologies. No equations, parameters, or derivations in the provided text reduce by construction to self-defined inputs, fitted subsets renamed as predictions, or self-citation chains. The central quantification relies on external network data and standard EON capabilities rather than internal redefinitions, satisfying the self-contained benchmark.

Axiom & Free-Parameter Ledger

0 free parameters · 1 axioms · 0 invented entities

Paper relies on standard domain assumptions about network topologies and EON capabilities; no free parameters, new axioms, or invented entities are described in the abstract.

axioms (1)
  • domain assumption Realistic case-study network topologies accurately represent 5G transport networks.
    Invoked when stating that numerical evaluation quantifies savings on these topologies.

pith-pipeline@v0.9.0 · 5802 in / 1149 out tokens · 28085 ms · 2026-05-25T16:35:11.807845+00:00 · methodology

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Reference graph

Works this paper leans on

45 extracted references · 45 canonical work pages

  1. [1]

    Flexible architectures for optical transport nodes and networks,

    S. Gringeri, B. Basch, V . Shukla, R. Egorov, and T. J. Xia, “Flexible architectures for optical transport nodes and networks,” IEEE Commu- nications Magazine , vol. 48, no. 7, pp. 40–50, 2010

    work page 2010

  2. [2]

    Towards fifth-generation (5G) optical transport networks,

    S. Aleksic, “Towards fifth-generation (5G) optical transport networks,” in Proceedings of International Conference on Transparent Optical Networks (ICTON) , July 2015, pp. 1–4

    work page 2015

  3. [3]

    Elastic optical networking for 5G transport,

    R. Boutaba, N. Shahriar, and S. Fathi, “Elastic optical networking for 5G transport,” Journal of Network and Systems Management , vol. 25, no. 4, pp. 819–847, 2017

    work page 2017

  4. [4]

    Network slicing in 5G: Survey and challenges,

    X. Foukas, G. Patounas, A. Elmokashfi, and M. K. Marina, “Network slicing in 5G: Survey and challenges,” IEEE Communications Magazine, vol. 55, no. 5, pp. 94–100, 2017

    work page 2017

  5. [5]

    Dynamic resource allocation in metro elastic optical networks using lyapunov drift optimization,

    M. Hadi, M. R. Pakravan, and E. Agrell, “Dynamic resource allocation in metro elastic optical networks using lyapunov drift optimization,” Journal of Optical Communications and Networking , vol. 11, no. 6, pp. 250–259, 2019

    work page 2019

  6. [6]

    Meeting 5G transport requirements with FlexE,

    “Meeting 5G transport requirements with FlexE,” White paper, ZTE, 2018

    work page 2018

  7. [7]

    Degraded-service-aware multipath pro- visioning in telecom mesh networks,

    R. Roy and B. Mukherjee, “Degraded-service-aware multipath pro- visioning in telecom mesh networks,” in Proceedings of IEEE/OSA OFC/NFOEC, Feb 2008, pp. 1–3

    work page 2008

  8. [8]

    Bandwidth squeezed restoration in spectrum- sliced elastic optical path networks (slice),

    Y . Sone, A. Watanabe, W. Imajuku, Y . Tsukishima, B. Kozicki, H. Takara, and M. Jinno, “Bandwidth squeezed restoration in spectrum- sliced elastic optical path networks (slice),” IEEE/OSA Journal of Optical Communications and Networking , vol. 3, no. 3, pp. 223–233, 2011

    work page 2011

  9. [9]

    Optimal design for shared backup path protected elastic optical networks under single-link failure,

    G. Shen, Y . Wei, and S. Bose, “Optimal design for shared backup path protected elastic optical networks under single-link failure,” IEEE/OSA Journal of Optical Communications and Networking , vol. 6, no. 7, pp. 649–659, 2014

    work page 2014

  10. [10]

    Flexible availability-aware differentiated pro- tection in software-defined elastic optical networks,

    X. Chen, M. Tornatore, S. Zhu, F. Ji, W. Zhou, C. Chen, D. Hu, L. Jiang, and Z. Zhu, “Flexible availability-aware differentiated pro- tection in software-defined elastic optical networks,” IEEE/OSA Journal of Lightwave Technology , vol. 33, no. 18, pp. 3872–3882, 2015

    work page 2015

  11. [11]

    Network virtualization over elastic optical networks with different protection schemes,

    K. D. R. Assis, S. Peng, R. C. Almeida, H. Waldman, A. Hammad, A. F. Santos, and D. Simeonidou, “Network virtualization over elastic optical networks with different protection schemes,” IEEE/OSA Journal of Optical Communication and Networking , vol. 8, no. 4, pp. 272–281, Apr 2016

    work page 2016

  12. [12]

    Survivable multipath pro- visioning with differential delay constraint in telecom mesh networks,

    S. Huang, C. U. Martel, and B. Mukherjee, “Survivable multipath pro- visioning with differential delay constraint in telecom mesh networks,” IEEE/ACM Transactions on Networking , vol. 19, no. 3, pp. 657–669, Jun. 2011

    work page 2011

  13. [13]

    SiM- PLE: Survivability in multi-path link embedding,

    M. M. A. Khan, N. Shahriar, R. Ahmed, and R. Boutaba, “SiM- PLE: Survivability in multi-path link embedding,” in Proceedings of IEEE/ACM/IFIP CNSM, 2015, pp. 210–218

    work page 2015

  14. [14]

    Characterization of failures in an ip backbone,

    A. Markopoulou, G. Iannaccone, S. Bhattacharyya, C.-N. Chuah, and C. Diot, “Characterization of failures in an ip backbone,” in Proceedings of IEEE INFOCOM 2004 , vol. 4, 2004, pp. 2307–2317

    work page 2004

  15. [15]

    Survivable virtual network embedding,

    M. R. Rahman, I. Aib, and R. Boutaba, “Survivable virtual network embedding,” in NETWORKING 2010 . Springer, 2010, pp. 40–52

    work page 2010

  16. [16]

    Survivable wdm mesh networks,

    S. Ramamurthy, L. Sahasrabuddhe, and B. Mukherjee, “Survivable wdm mesh networks,” IEEE/OSA Journal of Lightwave Technology , vol. 21, no. 4, p. 870, 2003

    work page 2003

  17. [17]

    Single-path provision- ing with multi-path recovery in flexgrid optical networks,

    A. Castro, L. Velasco, M. Ruiz, and J. Comellas, “Single-path provision- ing with multi-path recovery in flexgrid optical networks,” in Proceed- ings of International Congress on Ultra Modern Telecommunications and Control Systems , 2012, pp. 745–751

    work page 2012

  18. [18]

    Survivable traffic grooming in elastic optical networks—shared protection,

    M. Liu, M. Tornatore, and B. Mukherjee, “Survivable traffic grooming in elastic optical networks—shared protection,” Journal of lightwave technology, vol. 31, no. 6, pp. 903–909, 2013

    work page 2013

  19. [19]

    Survivable virtual optical network mapping in elastic optical networks with shared backup path protection,

    Y . Wang, X. Li, B. Guo, T. Gao, W. Li, and S. Huang, “Survivable virtual optical network mapping in elastic optical networks with shared backup path protection,” in 25th Wireless and Optical Communication Conference (WOCC), 2016, pp. 1–4

    work page 2016

  20. [20]

    Multicast routing and distance-adaptive spectrum allocation in elastic optical networks with shared protection,

    A. Cai, J. Guo, R. Lin, G. Shen, and M. Zukerman, “Multicast routing and distance-adaptive spectrum allocation in elastic optical networks with shared protection,” IEEE/OSA Journal of Lightwave Technology , vol. 34, no. 17, pp. 4076–4088, 2016

    work page 2016

  21. [21]

    Shared-protection survivable multipath scheme in flexible-grid optical networks against multiple failures,

    S. Yin, S. Huang, B. Guo, Y . Zhou, H. Huang, M. Zhang, Y . Zhao, J. Zhang, and W. Gu, “Shared-protection survivable multipath scheme in flexible-grid optical networks against multiple failures,” Journal of Lightwave Technology, vol. 35, no. 2, pp. 201–211, 2016

    work page 2016

  22. [22]

    Survivable virtual concatenation for data over sonet/sdh in optical transport networks,

    C. Ou, L. H. Sahasrabuddhe, K. Zhu, C. U. Martel, and B. Mukherjee, “Survivable virtual concatenation for data over sonet/sdh in optical transport networks,” IEEE/ACM Transactions on Networking (TON) , vol. 14, no. 1, pp. 218–231, 2006

    work page 2006

  23. [23]

    Capacity design of fast path restorable optical networks,

    O. Hauser, M. Kodialam, and T. Lakshman, “Capacity design of fast path restorable optical networks,” in Proceedings. Twenty-First Annual Joint Conference of the IEEE Computer and Communications Societies , vol. 2. IEEE, 2002, pp. 817–826

    work page 2002

  24. [24]

    A genetic algorithm for solving rsa problem in elastic optical networks with dedicated path protection,

    M. Klinkowski, “A genetic algorithm for solving rsa problem in elastic optical networks with dedicated path protection,” in Proceedings of In- ternational Joint Conference CISIS’12-ICEUTE´ 12-SOCO´ 12 Special Sessions, 2013, pp. 167–176

    work page 2013

  25. [25]

    An evolutionary algorithm approach for dedicated path protection problem in elastic optical networks,

    M. Klinkowski, “An evolutionary algorithm approach for dedicated path protection problem in elastic optical networks,” Cybernetics and Systems, vol. 44, no. 6-7, pp. 589–605, 2013

    work page 2013

  26. [26]

    Routing and spectrum allocation algorithms for elastic optical networks with dedicated path protection,

    K. Walkowiak, M. Klinkowski, B. Rabiega, and R. Go ´scie´n, “Routing and spectrum allocation algorithms for elastic optical networks with dedicated path protection,” Elsevier Optical Switching and Networking , vol. 13, pp. 63–75, 2014

    work page 2014

  27. [27]

    Survivable impairment-constrained virtual optical network mapping in flexible-grid optical networks,

    W. Xie, J. P. Jue, Q. Zhang, X. Wang, Q. She, P. Palacharla, and M. Sekiya, “Survivable impairment-constrained virtual optical network mapping in flexible-grid optical networks,” IEEE/OSA Journal of Optical Communications and Networking , vol. 6, no. 11, pp. 1008–1017, 2014

    work page 2014

  28. [28]

    Cost- effective survivable virtual optical network mapping in flexible band- width optical networks,

    B. Chen, J. Zhang, W. Xie, J. P. Jue, Y . Zhao, and G. Shen, “Cost- effective survivable virtual optical network mapping in flexible band- width optical networks,” IEEE/OSA Journal of Lightwave Technology , vol. 34, no. 10, pp. 2398–2412, 2016

    work page 2016

  29. [29]

    Energy efficiency with sliceable multi-flow transponders and elastic regenerators in surviv- able virtual optical networks,

    Y . Zhao, B. Chen, J. Zhang, and X. Wang, “Energy efficiency with sliceable multi-flow transponders and elastic regenerators in surviv- able virtual optical networks,” IEEE Transactions on Communications , vol. 64, no. 6, pp. 2539–2550, 2016

    work page 2016

  30. [30]

    Survivable multipath routing of anycast and unicast traffic in elastic optical networks,

    R. Go ´scie´n, K. Walkowiak, and M. Tornatore, “Survivable multipath routing of anycast and unicast traffic in elastic optical networks,” IEEE/OSA Journal of Optical Communications and Networking , vol. 8, no. 6, pp. 343–355, 2016

    work page 2016

  31. [31]

    Survivable multipath routing and spectrum allocation in OFDM-based flexible optical networks,

    L. Ruan and N. Xiao, “Survivable multipath routing and spectrum allocation in OFDM-based flexible optical networks,” Journal of Optical Communications and Networking , vol. 5, no. 3, pp. 172–182, 2013

    work page 2013

  32. [32]

    A survey on OFDM-based elastic core optical networking,

    G. Zhang, M. De Leenheer, A. Morea, and B. Mukherjee, “A survey on OFDM-based elastic core optical networking,” IEEE Communications Surveys & Tutorials , vol. 15, no. 1, pp. 65–87, 2012

    work page 2012

  33. [33]

    Optimal route, spectrum, and modulation level assignment in split-spectrum-enabled dynamic elastic optical networks,

    A. Pag `es, J. Perell ´o, S. Spadaro, and J. Comellas, “Optimal route, spectrum, and modulation level assignment in split-spectrum-enabled dynamic elastic optical networks,” IEEE/OSA Journal of Optical Com- munications and Networking , vol. 6, no. 2, pp. 114–126, 2014

    work page 2014

  34. [34]

    Achieving a fully-flexible virtual network embedding in elastic optical networks,

    N. Shahriar, S. Taeb, S. R. Chowdhury, M. Tornatore, R. Boutaba, J. Mitra, and M. Hemmati, “Achieving a fully-flexible virtual network embedding in elastic optical networks,” in IEEE INFOCOM , 2019

    work page 2019

  35. [35]

    Vcat-lcas in a clamshell,

    G. Bernstein, D. Caviglia, R. Rabbat, and H. Van Helvoort, “Vcat-lcas in a clamshell,” IEEE Communications Magazine , vol. 44, no. 5, pp. 34–36, 2006

    work page 2006

  36. [36]

    Optical internetworking forum - flex ethernet implementation agreement 1.1,

    “Optical internetworking forum - flex ethernet implementation agreement 1.1,” June 2017. [Online]. Available: https://www.oiforum. com/wp-content/uploads/2019/01/FLEXE1.1.pdf

    work page 2017

  37. [37]

    Virtual network embedding with coordinated node and link mapping,

    N. M. K. Chowdhury, M. R. Rahman, and R. Boutaba, “Virtual network embedding with coordinated node and link mapping,” in Proceedings of IEEE INFOCOM , 2009, pp. 783–791

    work page 2009

  38. [38]

    A study of the routing and spectrum allo- cation in spectrum-sliced elastic optical path networks,

    Y . Wang, X. Cao, and Y . Pan, “A study of the routing and spectrum allo- cation in spectrum-sliced elastic optical path networks,” in Proceedings of IEEE INFOCOM , 2011, pp. 1503–1511

    work page 2011

  39. [39]

    Routing and spectrum allocation in elastic optical networks: A tutorial,

    B. C. Chatterjee, N. Sarma, and E. Oki, “Routing and spectrum allocation in elastic optical networks: A tutorial,” IEEE Communications Surveys & Tutorials , vol. 17, no. 3, pp. 1776–1800, 2015

    work page 2015

  40. [40]

    Introductory combinatorics,

    R. A. Brualdi, “Introductory combinatorics,” New York, vol. 3, 1992

    work page 1992

  41. [41]

    Sndlib repository [online] http://sndlib.zib.de/home.action

    work page

  42. [42]

    spectral grids for WDM applications: DWDM frequency grid.[online] https://www.itu.int/rec/t-rec-g.694.1/en

    ITU-T G.694.1. spectral grids for WDM applications: DWDM frequency grid.[online] https://www.itu.int/rec/t-rec-g.694.1/en. APPENDIX A ALG. 2 OPTIMALITY PROOF Theorem 2. Alg. 2 returns a VLink ordering with the minimum commonality index. Proof. Suppose VLink orderingo which is generated by Alg. 2 does not have the minimum commonality index, therefore, ther...

    work page

  43. [43]

    A = {¯eo∗ i |1 ≤ i < j} which includes all the VLinks that come before ¯eo∗ j in both o∗ and o∗ 1

    work page

  44. [44]

    B = {¯eo∗ i |j <i ≤imax} which contains all the VLinks that come after ¯eo∗ j in o∗, but before ¯eo∗ j in o∗ 1

    work page

  45. [45]

    C = {¯eo∗ i |imax < i≤ | ¯E|} which includes the VLinks that come after ¯eo∗ j in both o∗ and o∗ 1. Fig. 6. Dividing the VLinks into 3 groups to check their commonality indexes From (9), we know that the effective commonality of each VLink only depends on the preceding VLinks. Hence, consid- ering that the set of preceding VLinks is the same ∀¯ei ∈A∪C in ...

    work page