Fiber Optic Networks
Source: https://link.springer.com/content/pdf/10.1007/978-1-4757-6048-4_45.pdf
For much of this class on networks we have considered simple graphs with simple problems. An example of more complex graph theory is that of fiber-optic networks. The scientific article “ROUTING IN ALL-OPTICAL NETWORKS: ALGORITHMIC AND GRAPH-THEORETIC PROBLEMS” by Luisa Gargano and Ugo Vaccaro from Dipartimento di Informatica ed Applicazioni, Universita di Salerno 84081 Baronissi (SA), Italy, linked above, delves into some nuances in graph theory specific to fiber optic networks.
Optical fibers are dielectric waveguides that are capable of propagating light over long distances at very high speeds with very little loss. They are used in the communication industry for these attributes – achieving near terabit per second data transmission rates. Fios by Verizon, for example, is an acronym for Fiber Optic Service, and is an all fiber network that provides television, internet, and phone services to over 5 million U.S residents
Fiber optic communication is revolutionizing the telecommunications industry, but there are a few networking problems that must be dealt with for all-optical networks to become more viable. In the article, nodes are considered to be routing links (locations where light signals are amplified or processed), and edges are the directed fiber optic cables themselves. This can be considered a directed graph, just like the email graphs covered in class.
A complication occurs when one considers what the significance of each edge is – each edge is a fiber optic cable that transmits signals over multiple wavelengths independently (through Wavelength Division Multiplexing – WDM). Any given edge can only transmit one signal of a given wavelength, otherwise the signals would be indiscernible. The simplest “network” with WDM would be to consider a graph with only two nodes – that way each signal would be transferred over a separate wavelength and it would be very simple. WDM poses an issue when there are many nodes (multiple routing links interconnect) – the one signal per wavelength must maintain across multiple routing links. Some wavelengths can be translated using converters, but these are expensive and as such would not be used at every node.
All of this culminates into a set of rather complex graph problems – one such problem covered in the article is the “Minimum Sufficient Set Problem”. It is to “Find a set of nodes S <; V such that if converters are placed only in the nodes in S then any set of dipaths P can be colored with L(P) colors The goal is to minimize the size of S.”
All of this serves to illustrate that specific networks, such as all-optical communications networks, can become very complicated when all factors are considered. Graph theory becomes extremely important when it comes to optimizing and building massive fiber-optic communication networks, but it also becomes extremely complex.