A. McCurdy, A. Shelton, B. Burns, C. Bayly, E. Handa, G. Gerstell, J.-M. Fortain, J.-P. Joensuu, L. Duvernay, R. Lingle, and S. Ash, “Submarine telecoms industry report,” Submarine Telecoms Forum, Inc., Tech. Rep., (2018).

M. Bardi and I. Capuzzo-Dolcetta, Optimal Control and Viscosity Solutions of Hamilton-Jacobi-Bellman Equations (Springer Science & Business Media, 2008).

L. Carter, D. Burnett, S. Drew, G. Marle, L. Hagadorn, D. Bartlett-McNeil, and N. Irvine, Submarine cables and the oceans: connecting the world (UNEP-WCMC Biodiversity Series No.31. ICPC/UNEP/UNEP-WCMC, 2009).

A. McCurdy, A. Shelton, B. Burns, C. Bayly, E. Handa, G. Gerstell, J.-M. Fortain, J.-P. Joensuu, L. Duvernay, R. Lingle, and S. Ash, “Submarine telecoms industry report,” Submarine Telecoms Forum, Inc., Tech. Rep., (2018).

D. R. Burnett, R. Beckman, and T. M. Davenport, Submarine Cables: The Handbook of Law and Policy (Martinus Nijhoff Publishers, 2013).

[Crossref]

C. Cao, Z. Wang, M. Zukerman, J. H. Manton, A. Bensoussan, and Y. Wang, “Optimal cable laying across an earthquake fault line considering elliptical failures,” IEEE Trans. Rel. 65(3), 1536–1550 (2016).

[Crossref]

R. Rapp, M. Lawrence, D. Borwick, and T. Kuwabara, “Marine survey & cable routing,” in Proc. SubOptic, (2004).

D. Burago, Y. Burago, and S. Ivanov, A Course in Metric Geometry (American Mathematical Society Providence, 2001).

D. Burago, Y. Burago, and S. Ivanov, A Course in Metric Geometry (American Mathematical Society Providence, 2001).

L. Carter, D. Burnett, S. Drew, G. Marle, L. Hagadorn, D. Bartlett-McNeil, and N. Irvine, Submarine cables and the oceans: connecting the world (UNEP-WCMC Biodiversity Series No.31. ICPC/UNEP/UNEP-WCMC, 2009).

D. R. Burnett, R. Beckman, and T. M. Davenport, Submarine Cables: The Handbook of Law and Policy (Martinus Nijhoff Publishers, 2013).

[Crossref]

A. McCurdy, A. Shelton, B. Burns, C. Bayly, E. Handa, G. Gerstell, J.-M. Fortain, J.-P. Joensuu, L. Duvernay, R. Lingle, and S. Ash, “Submarine telecoms industry report,” Submarine Telecoms Forum, Inc., Tech. Rep., (2018).

C. Cao, Z. Wang, M. Zukerman, J. H. Manton, A. Bensoussan, and Y. Wang, “Optimal cable laying across an earthquake fault line considering elliptical failures,” IEEE Trans. Rel. 65(3), 1536–1550 (2016).

[Crossref]

C. Cao, M. Zukerman, W. Wu, J. H. Manton, and B. Moran, “Survivable topology design of submarine networks,” J. Lightwave Technol. 31(5), 715–730 (2013).

[Crossref]

C. Cao, “Cost effective and survivable cabling design under major disasters,” Ph.D dissertation, City University of Hong Kong, (2015).

M. Bardi and I. Capuzzo-Dolcetta, Optimal Control and Viscosity Solutions of Hamilton-Jacobi-Bellman Equations (Springer Science & Business Media, 2008).

L. Carter, D. Burnett, S. Drew, G. Marle, L. Hagadorn, D. Bartlett-McNeil, and N. Irvine, Submarine cables and the oceans: connecting the world (UNEP-WCMC Biodiversity Series No.31. ICPC/UNEP/UNEP-WCMC, 2009).

S. Huang, E. Chen, and J. Guo, “Efficient seafloor classification and submarine cable route design using an autonomous underwater vehicle,” IEEE J. Oceanic Eng. 43(1), 7–18 (2018).

[Crossref]

M. Zhao, T. W. S. Chow, P. Tang, Z. Wang, J. Guo, and M. Zukerman, “Route selection for cabling considering cost minimization and earthquake survivability via a semi-supervised probabilistic model,” IEEE Trans. Ind. Informat. 13(2), 502–511 (2017).

[Crossref]

M. G. Crandall and P-L. Lions, “Viscosity solutions of Hamilton-Jacobi equations,” Trans. Am. Math. Soc. 277(1), 1–42 (1983).

[Crossref]

D. R. Burnett, R. Beckman, and T. M. Davenport, Submarine Cables: The Handbook of Law and Policy (Martinus Nijhoff Publishers, 2013).

[Crossref]

L. Carter, D. Burnett, S. Drew, G. Marle, L. Hagadorn, D. Bartlett-McNeil, and N. Irvine, Submarine cables and the oceans: connecting the world (UNEP-WCMC Biodiversity Series No.31. ICPC/UNEP/UNEP-WCMC, 2009).

T. P. Dübendorfer, “Impact analysis, early detection and mitigation of large-scale Internet attacks,” Ph.D dissertation, Dipl. Informatik-Ing., ETH Zürich, Zürich, Switzerland (2005).

A. McCurdy, A. Shelton, B. Burns, C. Bayly, E. Handa, G. Gerstell, J.-M. Fortain, J.-P. Joensuu, L. Duvernay, R. Lingle, and S. Ash, “Submarine telecoms industry report,” Submarine Telecoms Forum, Inc., Tech. Rep., (2018).

K. Eriksson, D. Estep, and C. Johnson, Applied Mathematics: Body and Soul: Derivatives and Geometry in IR3 (Springer, 2004).

K. Eriksson, D. Estep, and C. Johnson, Applied Mathematics: Body and Soul: Derivatives and Geometry in IR3 (Springer, 2004).

W. H. Press, S. A. Teukolsky, W. T. Vetterling, and B. P. Flannery, Numerical Recipes in C: The Art of Scientific Computing (Cambridge University, 1992).

A. McCurdy, A. Shelton, B. Burns, C. Bayly, E. Handa, G. Gerstell, J.-M. Fortain, J.-P. Joensuu, L. Duvernay, R. Lingle, and S. Ash, “Submarine telecoms industry report,” Submarine Telecoms Forum, Inc., Tech. Rep., (2018).

A. McCurdy, A. Shelton, B. Burns, C. Bayly, E. Handa, G. Gerstell, J.-M. Fortain, J.-P. Joensuu, L. Duvernay, R. Lingle, and S. Ash, “Submarine telecoms industry report,” Submarine Telecoms Forum, Inc., Tech. Rep., (2018).

S. Huang, E. Chen, and J. Guo, “Efficient seafloor classification and submarine cable route design using an autonomous underwater vehicle,” IEEE J. Oceanic Eng. 43(1), 7–18 (2018).

[Crossref]

M. Zhao, T. W. S. Chow, P. Tang, Z. Wang, J. Guo, and M. Zukerman, “Route selection for cabling considering cost minimization and earthquake survivability via a semi-supervised probabilistic model,” IEEE Trans. Ind. Informat. 13(2), 502–511 (2017).

[Crossref]

Z. Wang, Q. Wang, M. Zukerman, J. Guo, Y. Wang, G. Wang, J. Yang, and B. Moran, “Multiobjective path optimization for critical infrastructure links with consideration to seismic resilience,” Comput-Aided. Civ. Inf. 32(10), 836–855 (2017).

[Crossref]

L. Carter, D. Burnett, S. Drew, G. Marle, L. Hagadorn, D. Bartlett-McNeil, and N. Irvine, Submarine cables and the oceans: connecting the world (UNEP-WCMC Biodiversity Series No.31. ICPC/UNEP/UNEP-WCMC, 2009).

A. McCurdy, A. Shelton, B. Burns, C. Bayly, E. Handa, G. Gerstell, J.-M. Fortain, J.-P. Joensuu, L. Duvernay, R. Lingle, and S. Ash, “Submarine telecoms industry report,” Submarine Telecoms Forum, Inc., Tech. Rep., (2018).

J. Zhang, E. Modiano, and D. Hay, “Enhancing network robustness via shielding,” IEEE/ACM Trans. Netw. 25(4), 2209–2222 (2017).

[Crossref]

J. Hecht, “The bandwidth bottleneck,” Nature 536(7615), 139–142 (2016).

[Crossref]
[PubMed]

S. Huang, E. Chen, and J. Guo, “Efficient seafloor classification and submarine cable route design using an autonomous underwater vehicle,” IEEE J. Oceanic Eng. 43(1), 7–18 (2018).

[Crossref]

L. Carter, D. Burnett, S. Drew, G. Marle, L. Hagadorn, D. Bartlett-McNeil, and N. Irvine, Submarine cables and the oceans: connecting the world (UNEP-WCMC Biodiversity Series No.31. ICPC/UNEP/UNEP-WCMC, 2009).

D. Burago, Y. Burago, and S. Ivanov, A Course in Metric Geometry (American Mathematical Society Providence, 2001).

A. McCurdy, A. Shelton, B. Burns, C. Bayly, E. Handa, G. Gerstell, J.-M. Fortain, J.-P. Joensuu, L. Duvernay, R. Lingle, and S. Ash, “Submarine telecoms industry report,” Submarine Telecoms Forum, Inc., Tech. Rep., (2018).

K. Eriksson, D. Estep, and C. Johnson, Applied Mathematics: Body and Soul: Derivatives and Geometry in IR3 (Springer, 2004).

R. Rapp, M. Lawrence, D. Borwick, and T. Kuwabara, “Marine survey & cable routing,” in Proc. SubOptic, (2004).

R. Rapp, M. Lawrence, D. Borwick, and T. Kuwabara, “Marine survey & cable routing,” in Proc. SubOptic, (2004).

A. McCurdy, A. Shelton, B. Burns, C. Bayly, E. Handa, G. Gerstell, J.-M. Fortain, J.-P. Joensuu, L. Duvernay, R. Lingle, and S. Ash, “Submarine telecoms industry report,” Submarine Telecoms Forum, Inc., Tech. Rep., (2018).

M. G. Crandall and P-L. Lions, “Viscosity solutions of Hamilton-Jacobi equations,” Trans. Am. Math. Soc. 277(1), 1–42 (1983).

[Crossref]

C. Cao, Z. Wang, M. Zukerman, J. H. Manton, A. Bensoussan, and Y. Wang, “Optimal cable laying across an earthquake fault line considering elliptical failures,” IEEE Trans. Rel. 65(3), 1536–1550 (2016).

[Crossref]

C. Cao, M. Zukerman, W. Wu, J. H. Manton, and B. Moran, “Survivable topology design of submarine networks,” J. Lightwave Technol. 31(5), 715–730 (2013).

[Crossref]

W. Wu, B. Moran, J. H. Manton, and M. Zukerman, “Topology design of undersea cables considering survivability under major disasters,” in Proc. WAINA, 1154–1159 (2009).

L. Carter, D. Burnett, S. Drew, G. Marle, L. Hagadorn, D. Bartlett-McNeil, and N. Irvine, Submarine cables and the oceans: connecting the world (UNEP-WCMC Biodiversity Series No.31. ICPC/UNEP/UNEP-WCMC, 2009).

A. McCurdy, A. Shelton, B. Burns, C. Bayly, E. Handa, G. Gerstell, J.-M. Fortain, J.-P. Joensuu, L. Duvernay, R. Lingle, and S. Ash, “Submarine telecoms industry report,” Submarine Telecoms Forum, Inc., Tech. Rep., (2018).

J. Zhang, E. Modiano, and D. Hay, “Enhancing network robustness via shielding,” IEEE/ACM Trans. Netw. 25(4), 2209–2222 (2017).

[Crossref]

Z. Wang, Q. Wang, B. Moran, and M. Zukerman, “Application of the fast marching method for path planning of long-haul optical fiber cables with shielding,” IEEE Access 6(1), 41367–41378 (2018).

[Crossref]

Z. Wang, Q. Wang, M. Zukerman, and B. Moran, “A seismic resistant design algorithm for laying and shielding of optical fiber cables,” J. Lightwave Technol. 35(14), 3060–3074 (2017).

[Crossref]

Z. Wang, Q. Wang, M. Zukerman, J. Guo, Y. Wang, G. Wang, J. Yang, and B. Moran, “Multiobjective path optimization for critical infrastructure links with consideration to seismic resilience,” Comput-Aided. Civ. Inf. 32(10), 836–855 (2017).

[Crossref]

C. Cao, M. Zukerman, W. Wu, J. H. Manton, and B. Moran, “Survivable topology design of submarine networks,” J. Lightwave Technol. 31(5), 715–730 (2013).

[Crossref]

W. Wu, B. Moran, J. H. Manton, and M. Zukerman, “Topology design of undersea cables considering survivability under major disasters,” in Proc. WAINA, 1154–1159 (2009).

K. Nielsen, “Submarine telecoms industry report,” Submarine Telecoms Forum, Inc., Tech. Rep., (2015).

W. H. Press, S. A. Teukolsky, W. T. Vetterling, and B. P. Flannery, Numerical Recipes in C: The Art of Scientific Computing (Cambridge University, 1992).

R. Rapp, M. Lawrence, D. Borwick, and T. Kuwabara, “Marine survey & cable routing,” in Proc. SubOptic, (2004).

J. A. Sethian and A. Vladimirsky, “Ordered upwind methods for static Hamilton–Jacobi equations: Theory and algorithms,” SIAM J. Numer. Anal. 41(1), 325–363 (2003).

[Crossref]

J. A. Sethian and A. Vladimirsky, “Ordered upwind methods for static Hamilton–Jacobi equations,” PNAS. 98(20), 11069–11074 (2001).

[Crossref]
[PubMed]

A. McCurdy, A. Shelton, B. Burns, C. Bayly, E. Handa, G. Gerstell, J.-M. Fortain, J.-P. Joensuu, L. Duvernay, R. Lingle, and S. Ash, “Submarine telecoms industry report,” Submarine Telecoms Forum, Inc., Tech. Rep., (2018).

S. Smale, “Global analysis and economics I: Pareto optimum and a generalization of Morse theory,” The Collected Papers of Stephen Smale 1, 259–270 (2000).

[Crossref]

E. Tahchi and EGS (Asia) Limited, Quarry Bay, Hong Kong SAR, China (personal communication, 2018).

M. Zhao, T. W. S. Chow, P. Tang, Z. Wang, J. Guo, and M. Zukerman, “Route selection for cabling considering cost minimization and earthquake survivability via a semi-supervised probabilistic model,” IEEE Trans. Ind. Informat. 13(2), 502–511 (2017).

[Crossref]

W. H. Press, S. A. Teukolsky, W. T. Vetterling, and B. P. Flannery, Numerical Recipes in C: The Art of Scientific Computing (Cambridge University, 1992).

W. H. Press, S. A. Teukolsky, W. T. Vetterling, and B. P. Flannery, Numerical Recipes in C: The Art of Scientific Computing (Cambridge University, 1992).

J. A. Sethian and A. Vladimirsky, “Ordered upwind methods for static Hamilton–Jacobi equations: Theory and algorithms,” SIAM J. Numer. Anal. 41(1), 325–363 (2003).

[Crossref]

J. A. Sethian and A. Vladimirsky, “Ordered upwind methods for static Hamilton–Jacobi equations,” PNAS. 98(20), 11069–11074 (2001).

[Crossref]
[PubMed]

D. J. Wald, “Relationships between peak ground acceleration, peak ground velocity, and modified Mercalli intensity in California,” Earthq. Spectra. 15(3), 557–564 (1999).

[Crossref]

Z. Wang, Q. Wang, M. Zukerman, J. Guo, Y. Wang, G. Wang, J. Yang, and B. Moran, “Multiobjective path optimization for critical infrastructure links with consideration to seismic resilience,” Comput-Aided. Civ. Inf. 32(10), 836–855 (2017).

[Crossref]

Z. Wang, Q. Wang, B. Moran, and M. Zukerman, “Application of the fast marching method for path planning of long-haul optical fiber cables with shielding,” IEEE Access 6(1), 41367–41378 (2018).

[Crossref]

Z. Wang, Q. Wang, M. Zukerman, and B. Moran, “A seismic resistant design algorithm for laying and shielding of optical fiber cables,” J. Lightwave Technol. 35(14), 3060–3074 (2017).

[Crossref]

Z. Wang, Q. Wang, M. Zukerman, J. Guo, Y. Wang, G. Wang, J. Yang, and B. Moran, “Multiobjective path optimization for critical infrastructure links with consideration to seismic resilience,” Comput-Aided. Civ. Inf. 32(10), 836–855 (2017).

[Crossref]

Z. Wang, Q. Wang, M. Zukerman, J. Guo, Y. Wang, G. Wang, J. Yang, and B. Moran, “Multiobjective path optimization for critical infrastructure links with consideration to seismic resilience,” Comput-Aided. Civ. Inf. 32(10), 836–855 (2017).

[Crossref]

C. Cao, Z. Wang, M. Zukerman, J. H. Manton, A. Bensoussan, and Y. Wang, “Optimal cable laying across an earthquake fault line considering elliptical failures,” IEEE Trans. Rel. 65(3), 1536–1550 (2016).

[Crossref]

Z. Wang, Q. Wang, B. Moran, and M. Zukerman, “Application of the fast marching method for path planning of long-haul optical fiber cables with shielding,” IEEE Access 6(1), 41367–41378 (2018).

[Crossref]

Z. Wang, Q. Wang, M. Zukerman, and B. Moran, “A seismic resistant design algorithm for laying and shielding of optical fiber cables,” J. Lightwave Technol. 35(14), 3060–3074 (2017).

[Crossref]

Z. Wang, Q. Wang, M. Zukerman, J. Guo, Y. Wang, G. Wang, J. Yang, and B. Moran, “Multiobjective path optimization for critical infrastructure links with consideration to seismic resilience,” Comput-Aided. Civ. Inf. 32(10), 836–855 (2017).

[Crossref]

M. Zhao, T. W. S. Chow, P. Tang, Z. Wang, J. Guo, and M. Zukerman, “Route selection for cabling considering cost minimization and earthquake survivability via a semi-supervised probabilistic model,” IEEE Trans. Ind. Informat. 13(2), 502–511 (2017).

[Crossref]

C. Cao, Z. Wang, M. Zukerman, J. H. Manton, A. Bensoussan, and Y. Wang, “Optimal cable laying across an earthquake fault line considering elliptical failures,” IEEE Trans. Rel. 65(3), 1536–1550 (2016).

[Crossref]

C. Cao, M. Zukerman, W. Wu, J. H. Manton, and B. Moran, “Survivable topology design of submarine networks,” J. Lightwave Technol. 31(5), 715–730 (2013).

[Crossref]

W. Wu, B. Moran, J. H. Manton, and M. Zukerman, “Topology design of undersea cables considering survivability under major disasters,” in Proc. WAINA, 1154–1159 (2009).

Z. Wang, Q. Wang, M. Zukerman, J. Guo, Y. Wang, G. Wang, J. Yang, and B. Moran, “Multiobjective path optimization for critical infrastructure links with consideration to seismic resilience,” Comput-Aided. Civ. Inf. 32(10), 836–855 (2017).

[Crossref]

J. Zhang, E. Modiano, and D. Hay, “Enhancing network robustness via shielding,” IEEE/ACM Trans. Netw. 25(4), 2209–2222 (2017).

[Crossref]

M. Zhao, T. W. S. Chow, P. Tang, Z. Wang, J. Guo, and M. Zukerman, “Route selection for cabling considering cost minimization and earthquake survivability via a semi-supervised probabilistic model,” IEEE Trans. Ind. Informat. 13(2), 502–511 (2017).

[Crossref]

Z. Wang, Q. Wang, B. Moran, and M. Zukerman, “Application of the fast marching method for path planning of long-haul optical fiber cables with shielding,” IEEE Access 6(1), 41367–41378 (2018).

[Crossref]

Z. Wang, Q. Wang, M. Zukerman, and B. Moran, “A seismic resistant design algorithm for laying and shielding of optical fiber cables,” J. Lightwave Technol. 35(14), 3060–3074 (2017).

[Crossref]

M. Zhao, T. W. S. Chow, P. Tang, Z. Wang, J. Guo, and M. Zukerman, “Route selection for cabling considering cost minimization and earthquake survivability via a semi-supervised probabilistic model,” IEEE Trans. Ind. Informat. 13(2), 502–511 (2017).

[Crossref]

Z. Wang, Q. Wang, M. Zukerman, J. Guo, Y. Wang, G. Wang, J. Yang, and B. Moran, “Multiobjective path optimization for critical infrastructure links with consideration to seismic resilience,” Comput-Aided. Civ. Inf. 32(10), 836–855 (2017).

[Crossref]

D. L. Msongaleli, F. Dikbiyik, M. Zukerman, and B. Mukherjee, “Disaster-aware submarine fiber-optic cable deployment for mesh networks,” J. Lightwave Technol. 34(18), 4293–4303 (2016).

[Crossref]

C. Cao, Z. Wang, M. Zukerman, J. H. Manton, A. Bensoussan, and Y. Wang, “Optimal cable laying across an earthquake fault line considering elliptical failures,” IEEE Trans. Rel. 65(3), 1536–1550 (2016).

[Crossref]

C. Cao, M. Zukerman, W. Wu, J. H. Manton, and B. Moran, “Survivable topology design of submarine networks,” J. Lightwave Technol. 31(5), 715–730 (2013).

[Crossref]

W. Wu, B. Moran, J. H. Manton, and M. Zukerman, “Topology design of undersea cables considering survivability under major disasters,” in Proc. WAINA, 1154–1159 (2009).

Z. Wang, Q. Wang, M. Zukerman, J. Guo, Y. Wang, G. Wang, J. Yang, and B. Moran, “Multiobjective path optimization for critical infrastructure links with consideration to seismic resilience,” Comput-Aided. Civ. Inf. 32(10), 836–855 (2017).

[Crossref]

D. J. Wald, “Relationships between peak ground acceleration, peak ground velocity, and modified Mercalli intensity in California,” Earthq. Spectra. 15(3), 557–564 (1999).

[Crossref]

Z. Wang, Q. Wang, B. Moran, and M. Zukerman, “Application of the fast marching method for path planning of long-haul optical fiber cables with shielding,” IEEE Access 6(1), 41367–41378 (2018).

[Crossref]

P. N. Tran and H. Saito, “Geographical route design of physical networks using earthquake risk information,” IEEE Commun. Mag. 54(7), 131–137 (2016).

[Crossref]

S. Huang, E. Chen, and J. Guo, “Efficient seafloor classification and submarine cable route design using an autonomous underwater vehicle,” IEEE J. Oceanic Eng. 43(1), 7–18 (2018).

[Crossref]

M. Zhao, T. W. S. Chow, P. Tang, Z. Wang, J. Guo, and M. Zukerman, “Route selection for cabling considering cost minimization and earthquake survivability via a semi-supervised probabilistic model,” IEEE Trans. Ind. Informat. 13(2), 502–511 (2017).

[Crossref]

C. Cao, Z. Wang, M. Zukerman, J. H. Manton, A. Bensoussan, and Y. Wang, “Optimal cable laying across an earthquake fault line considering elliptical failures,” IEEE Trans. Rel. 65(3), 1536–1550 (2016).

[Crossref]

H. Saito, “Analysis of geometric disaster evaluation model for physical networks,” IEEE/ACM Trans. Netw. 23(6), 1777–1789 (2014).

[Crossref]

J. Zhang, E. Modiano, and D. Hay, “Enhancing network robustness via shielding,” IEEE/ACM Trans. Netw. 25(4), 2209–2222 (2017).

[Crossref]

C. Cao, M. Zukerman, W. Wu, J. H. Manton, and B. Moran, “Survivable topology design of submarine networks,” J. Lightwave Technol. 31(5), 715–730 (2013).

[Crossref]

D. L. Msongaleli, F. Dikbiyik, M. Zukerman, and B. Mukherjee, “Disaster-aware submarine fiber-optic cable deployment for mesh networks,” J. Lightwave Technol. 34(18), 4293–4303 (2016).

[Crossref]

P. N. Tran and H. Saito, “Enhancing physical network robustness against earthquake disasters with additional links,” J. Lightwave Technol. 34(22), 5226–5238 (2016).

[Crossref]

Z. Wang, Q. Wang, M. Zukerman, and B. Moran, “A seismic resistant design algorithm for laying and shielding of optical fiber cables,” J. Lightwave Technol. 35(14), 3060–3074 (2017).

[Crossref]

J. Hecht, “The bandwidth bottleneck,” Nature 536(7615), 139–142 (2016).

[Crossref]
[PubMed]

J. A. Sethian and A. Vladimirsky, “Ordered upwind methods for static Hamilton–Jacobi equations,” PNAS. 98(20), 11069–11074 (2001).

[Crossref]
[PubMed]

J. A. Sethian and A. Vladimirsky, “Ordered upwind methods for static Hamilton–Jacobi equations: Theory and algorithms,” SIAM J. Numer. Anal. 41(1), 325–363 (2003).

[Crossref]

S. Smale, “Global analysis and economics I: Pareto optimum and a generalization of Morse theory,” The Collected Papers of Stephen Smale 1, 259–270 (2000).

[Crossref]

M. G. Crandall and P-L. Lions, “Viscosity solutions of Hamilton-Jacobi equations,” Trans. Am. Math. Soc. 277(1), 1–42 (1983).

[Crossref]

M. Bardi and I. Capuzzo-Dolcetta, Optimal Control and Viscosity Solutions of Hamilton-Jacobi-Bellman Equations (Springer Science & Business Media, 2008).

W. H. Press, S. A. Teukolsky, W. T. Vetterling, and B. P. Flannery, Numerical Recipes in C: The Art of Scientific Computing (Cambridge University, 1992).

C. Cao, “Cost effective and survivable cabling design under major disasters,” Ph.D dissertation, City University of Hong Kong, (2015).

W. Wu, B. Moran, J. H. Manton, and M. Zukerman, “Topology design of undersea cables considering survivability under major disasters,” in Proc. WAINA, 1154–1159 (2009).

D. Burago, Y. Burago, and S. Ivanov, A Course in Metric Geometry (American Mathematical Society Providence, 2001).

K. Eriksson, D. Estep, and C. Johnson, Applied Mathematics: Body and Soul: Derivatives and Geometry in IR3 (Springer, 2004).

K. Nielsen, “Submarine telecoms industry report,” Submarine Telecoms Forum, Inc., Tech. Rep., (2015).

E. Tahchi and EGS (Asia) Limited, Quarry Bay, Hong Kong SAR, China (personal communication, 2018).

L. Carter, D. Burnett, S. Drew, G. Marle, L. Hagadorn, D. Bartlett-McNeil, and N. Irvine, Submarine cables and the oceans: connecting the world (UNEP-WCMC Biodiversity Series No.31. ICPC/UNEP/UNEP-WCMC, 2009).

S. Chattopadhyaya, “New submarine cable for digital Africa! How to build! Who will build!” (2018), https://www.submarinenetworks.com/en/insights/ .

A. McCurdy, A. Shelton, B. Burns, C. Bayly, E. Handa, G. Gerstell, J.-M. Fortain, J.-P. Joensuu, L. Duvernay, R. Lingle, and S. Ash, “Submarine telecoms industry report,” Submarine Telecoms Forum, Inc., Tech. Rep., (2018).

mi2g, “More than 1% GDP drop estimated per week of Internet blackout,” (2005), http://www.mi2g.com .

T. P. Dübendorfer, “Impact analysis, early detection and mitigation of large-scale Internet attacks,” Ph.D dissertation, Dipl. Informatik-Ing., ETH Zürich, Zürich, Switzerland (2005).

W. Qiu, “Submarine cables cut after Taiwan earthquake in Dec 2006,” (2011), http://www.submarinenetworks.com .

D. R. Burnett, R. Beckman, and T. M. Davenport, Submarine Cables: The Handbook of Law and Policy (Martinus Nijhoff Publishers, 2013).

[Crossref]

R. Rapp, M. Lawrence, D. Borwick, and T. Kuwabara, “Marine survey & cable routing,” in Proc. SubOptic, (2004).