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1 Routing and Wavelength Assignment in Wavelength Routing Networks

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2 Routing and Wavelength Assignment (RWA) Problem Given a set of connections, set up lightpaths by routing and assigning a wavelength to each connection Two constraints –Wavelength continuity constraint: a lightpath must use the same wavelength on all the links along its path –Distinct wavelength constraint: all lightpaths using the same link must be allocated distinct wavelengths

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3 Two Versions of RWA Static RWA –Set of connections known in advance –Goal is to minimize the number of wavelengths used Dynamic RWA –Connection requests arrive sequentially. –Setup a lightpath when a connection request arrives and teardown the lightpath after a finite amount of time –Goal is to minimize connection blocking

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4 Static RWA An ILP (see handout) –Solve routing and wavelength assignment jointly –Objective: minimize the maximum flow (flow = # lightpaths passing through a link) Use the ILP to obtain the min number of wavelengths required: –Pick a certain number of wavelengths, see if a solution can be found –No - increase the number of wavelengths until a solution can be found. –Yes - decrease the number of wavelengths until a solution can’t be found

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5 Static RWA Decompose into two sub-problems –Routing Formulated as ILP Objective: minimize the maximum number of lightpaths on any link –Wavelength assignment Reduce to graph coloring problem

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6 Static Wavelength Assignment Problem Given a set of lightpaths and their routes, assign a wavelength to each lightpath –Constraint: any two lightpaths sharing the same physical link are assigned different wavelengths –Objective: minimize the number of wavelengths used Problem can be reduced to graph coloring –Construct a graph G where nodes represents lightpaths, an edge exists between two nodes if the corresponding lightpaths pass through a common physical link –Color the nodes in G such that no two adjacent nodes have the same color

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7 Reduce Wavelength Assignment to Graph Coloring

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8 Graph Coloring NP-complete Sequential graph-coloring heuristic –Vertices sequentially added to the portion of the graph already colored –When add a vertex, assign it the smallest color not used by any of its neighbors Smallest-last ordering: assuming that the vertices v k+1,..., v n have been selected, choose v k so that the degree of v k in the subgraph induced by V - {v k+1,..., v n } is minimal.

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9 Wavelength Converters Wavelength converter: convert the wavelength of an input signal to a different wavelength Degree of Wavelength Conversion –Full wavelength conversion: any input wavelength can be converted to any other wavelength –Fixed wavelength conversion: an input wavelength can be converted to exactly one other wavelength –Limited wavelength conversion: an input wavelength can be converted to a subset of the available wavelengths

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10 Static RWA with Wavelength Conversion If each node has full wavelength conversion capability –Only need solve routing problem –Minimizing the maximum flow will minimize the number of wavelengths used

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11 Static RWA: a Layered Graph Approach Route and assign wavelength to each connection one by one Use layered graph to deal with wavelength continuity constraint –Create W copies of the network graph, W = number of wavelengths in a fiber –RWA is solved by finding a path in one copy of the network graph Limited/fixed conversion: add links between layers

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NP-Complete problems.

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