Optic fiber
Electronic switch
the fiber serves as a transmission medium
Optical networks - 1st generation
1. Optical networks – 1. Optical networks – basic notionsbasic notions
Routing in the optical domainTwo 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
Optical networks - 2nd generation
Optical switch
lightpathlightpath
OADM (optical add-drop multiplexer)
No two inputs with the same wavelength should be routed on the same edge.
• low capacity requests can be groomed into high capacity wavelengths (colors).
• colors can be assigned such that at most g lightpaths with the same color can share an edge
• g is the grooming factor
Traffic grooming
Optical networksOptical networks
ADMs, OADMs, ADMs, OADMs, groominggrooming
Graph theoretical Graph theoretical modelmodel
Coloring and routingColoring and routing
minADMminADM
Input:Input: a graph, a set of lightpaths, t>o. a graph, a set of lightpaths, t>o.
Output:Output: can the lightpath be colored such can the lightpath be colored such that #ADMs that #ADMs ≤ t ? t ?
2.1 minADM is NPC for a 2.1 minADM is NPC for a ringring
minADMminADM
Input:Input: a graph, a set of lightpaths, t>o. a graph, a set of lightpaths, t>o.
Output:Output: can the lightpath be colored such can the lightpath be colored such that #ADMs that #ADMs ≤ t ? t ?
Coloring of aColoring of a circular arc circular arc graphgraph
Not always possible with max Not always possible with max loadload
Input:Input: circular arc graph G, k>o. circular arc graph G, k>o.
Output:Output: can the arcs be colored by can the arcs be colored by ≤ k k colors?colors?
Coloring of a Coloring of a circular arc circular arc graphgraph
Coloring of a circular arc graphColoring of a circular arc graph Input:Input: circular arc graph G, k>o. circular arc graph G, k>o.
Output:Output: can the arcs be colored with can the arcs be colored with ≤ k k colors?colors?
minADMminADM
Input:Input: a graph, a set of lightpaths, a graph, a set of lightpaths, t>o.t>o.
Output:Output: can the lightpath be can the lightpath be colored such that #ADMs colored such that #ADMs ≤ t ? t ?
G
Claim:Claim: can color G with ≤ k colors
iff can color H with ≤ k colors
iff can color H with #ADMs ≤ N.
G H
Assume a coloring with ≤ 3 colors …
Claim:Claim: can color H with ≤ 3 colors iff
can color H with #ADMs ≤ 13
Claim:Claim: can color with ≤ 3 colors iff
can color the lightpaths with ≤ 13 ADMs
Assume a coloring with ≤ 13 ADMs …
#ADMs = N + #chains
N lightpaths
cycleschain
s
Cycles are good, chains are bad
A. Structure of a solutionA. Structure of a solution
In the approximation algorithms there are two common techniques for saving ADMs:
Eliminate cycles of lightpaths
Find matchings of lightpaths
#ADMs = N + #chains
cost(S) = N + chains=13+6=19–Every path costscosts 1 ADM
cost(S) = 2N-savings=26-7=19–Every connection savessaves 1 ADM
N lightpaths
N=13
w/out grooming:
ALG 2N N OPT
ALG 2 OPT
N: # of lightpathsALG: #ADMs used by algorithmOPT: #ADMs used by an optimal solution
w/ grooming:
ALG 2N N/g OPT
ALG 2g OPT
B. The competitive ratioB. The competitive ratio
Lemma: Assume that a solution ALG saves y ADMs, and OPT saves x ADMs.
x 1 if y then cost(ALG) (2- )cost(S*).
k k³ £
C. A basic C. A basic lemmalemma
x if y then
23
cost(S)
f or
cost(S*)
exa
2
mple: ³
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