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**Optical networks: Basics of WDM**

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**Optical networks - 1st generation**

the fiber serves as a transmission medium Electronic switch Optic fiber

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**Optical networks - 2nd generation**

Routing in the optical domain Two complementing technologies: - Wavelength Division Multiplexing (WDM): Transmission of data simultaneously at multiple wavelengths over same fiber - Optical switches: the output port is determined according to the input port and the wavelength

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**Wavelength Division Multiplexing (WDM)**

Directed: Optic Fiber Symmetric: Optic Fiber Undirected: Optic Fiber

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Optical Switches No two inputs with the same wavelength should be routed on the same edge.

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Lightpaths ADM ADM Data in electronic form Data in electronic form

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A virtual topology

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Lightpaths Valid coloring p1 p2

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**The Routing Problem Input : Output: A graph G=(V,E)**

A set or sequence of node pairs (ai,bi) Output: A set or sequence of paths pi =(ai, v1, …, bi)

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The Load Given a graph G=(V,E) and a set P of paths on the graph, we define: for any edge e of the graph: the load on this edge l(e)=|Pe| The (maximum, minimum, average) load on the network:

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**Wavelength Assignment Problem (WLA)**

Input: A graph G=(V,E). A set or sequence of paths P. Output: A coloring w of the paths: Constraint:

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**Routing and WLA (RLA/WRA)**

Input : A graph G=(V,E) A set or sequence of node pairs (ai,bi) Output: A set or sequence of paths pi =(ai, v1, …, bi) A coloring w of the paths: Constraint:

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**Cost Measure: # of colors**

For any legal coloring w of the paths:

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**Static vs. Dynamic vs. Incremental**

Static: The input is a set (of pairs or paths), the algorithm calculates its output based on the input. Incremental (Online): The input is a sequence of input elements (pairs or paths). It is supplied to the algorithm one element at a time. The output corresponding to the input element is calculated w/o knowledge of the subsequent input elements

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**Static vs. Dynamic vs. Incremental**

Similar to incremental The sequence may contain deletion requests for previous elements.

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**WLA (A trivial lower bound)**

For any instance of the WLA problem: W>=L. Proof: Consider an edge e, such that L=l(e). There are L paths p1, …, p|L| using e, because the paths are simple. Therefore :

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**WLA (A trivial lower bound)**

For some instances W > L. L=2 W=3

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**Static WLA on Path Topologies**

The GREEDY algorithm: // The set of integers for i = 1 to |V| do for each path p=(x,i) do for each path p=(i,x) do

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**Static WLA on Path Topologies**

Let the value of after node i is processed. Clearly, Prove by induction on i that Therefore:

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