## Wavelength Routing in All-Optical Tree Networks: A Survey (2001)

Venue: | Computers and Artificial Intelligence |

Citations: | 8 - 0 self |

### BibTeX

@ARTICLE{Caragiannis01wavelengthrouting,

author = {Ioannis Caragiannis and Christos Kaklamanis and Pino Persiano},

title = {Wavelength Routing in All-Optical Tree Networks: A Survey},

journal = {Computers and Artificial Intelligence},

year = {2001},

volume = {2001},

pages = {2001}

}

### OpenURL

### Abstract

We study the problem of allocating optical bandwidth to sets of communication requests in all--optical networks that utilize Wavelength Division Multiplexing (WDM). WDM technology establishes communication between pairs of network nodes by establishing transmitter--receiver paths and assigning wavelengths to each path so that no two paths going through the same fiber link use the same wavelength. Optical bandwidth is the number of distinct wavelengths. Since state--of--the--art technology allows for a limited number of wavelengths, the engineering problem to be solved is to establish communication between pairs of nodes so that the total number of wavelengths used is minimized; this is known as the wavelength routing problem. In this paper, we survey recent advances in bandwidth allocation in tree--shaped WDM all-- optical networks: -- We present hardness results and lower bounds for the general problem and the special case of symmetric communication. -- We give the main ideas of deterministic greedy algorithms and study their limitations. -- We demonstrate how we can achieve optimal and nearly--optimal bandwidth utilization in networks with wavelength converters using simple algorithms. -- We also present recent results about the use of randomization for wavelength routing. 1

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Citation Context ...ortant engineering problem to be solved is to establish communication between pairs of nodes so that the total number of wavelengths used is minimized; this is known as the wavelength routing problem =-=[1, 34]-=-. Given a pattern of communication requests and a corresponding path for each request, we define the load of the pattern as the maximum number of requests that traverse any fiber of the network. For t... |

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Citation Context ...es of the converter depicted in Figure 8 has asymptotically optimal degree, the total number of possible conversions is too large. Auletta et al. [7] (see also [3]), extending techniques presented in =-=[36]-=-, construct wavelength converters of small size that allow for optimal and nearly--optimal conversion on binary trees. The construction is based on properties of dispersers [42] and Ramanujan graphs, ... |

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Citation Context ...echniques presented in [36], construct wavelength converters of small size that allow for optimal and nearly--optimal conversion on binary trees. The construction is based on properties of dispersers =-=[42]-=- and Ramanujan graphs, which have been explicitly constructed in [30, 31, 45]. Theorem 17 (Auletta et al. [7], see also [3]) There exist converters of size O i L log 2 L log log L j that allow greedy ... |

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Citation Context ...ch tree of the forest, independently. 11 We proceed by considering the application of the greedy algorithm to spiders; a spider is a tree having at most one node of degree greater than 2. It is known =-=[20, 46]-=- that spiders guarantee optimal bandwidth utilization. In [3], it is demonstrated how this can be achieved by a greedy algorithm. Notice that the tree depicted in Figure 1 is the smallest tree that is... |

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Citation Context ...ble to greedily route any communication pattern of load at most (1 \Gamma ffl)W . 6 Randomized Algorithms In an attempt to beat the 5=3 lower bound for deterministic greedy algorithms, Auletta et al. =-=[4]-=- define the class of randomized greedy wavelength routing algorithms. Randomized greedy algorithms have the same structure as deterministic ones; that is, starting from a node, they consider the nodes... |

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Citation Context ... least 5L=4 necessary wavelengths. As we will see below (Section 4), these statements hold for the special case of symmetric communication. 3 Greedy Algorithms All known wavelength routing algorithms =-=[15, 22, 23, 24, 28, 32]-=- belong to a special class of algorithms, the class of greedy algorithms. We devote this section to their study. Given a tree network T and a pattern of requests P , we call greedy a wavelength routin... |

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Citation Context ...ts about optimal and nearly--optimal bandwidth utilization in all--pairs and down conversion trees. All results make use of the expansion properties of Ramanujan graphs. The interested reader may see =-=[3, 6, 19]-=- for a complete discussion and proofs. Gargano [19] and independently Auletta et al. [6] (see also [3]) show that using Ramanujan graphs of constant degree, we can achieve optimal bandwidth utilizatio... |

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Citation Context ... differences between the general wavelength routing problem and the case where the input instance is restricted to patterns of symmetric communication requests. For these patterns, Caragiannis et al. =-=[13]-=- have proved some interesting statements (lower bounds). Both NP--completeness results (Theorems 1 and 2) hold in the case of symmetric patterns of communication requests [13]. Notice that the lower b... |

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Citation Context ... least 5L=4 necessary wavelengths. As we will see below (Section 4), these statements hold for the special case of symmetric communication. 3 Greedy Algorithms All known wavelength routing algorithms =-=[15, 22, 23, 24, 28, 32]-=- belong to a special class of algorithms, the class of greedy algorithms. We devote this section to their study. Given a tree network T and a pattern of requests P , we call greedy a wavelength routin... |

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Citation Context ...ncentrator produced by putting back--to--back two copies of the converter depicted in Figure 8 has asymptotically optimal degree, the total number of possible conversions is too large. Auletta et al. =-=[7]-=- (see also [3]), extending techniques presented in [36], construct wavelength converters of small size that allow for optimal and nearly--optimal conversion on binary trees. The construction is based ... |

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Citation Context ... one might think of bipartite edge coloring problems with different constraints. Tight bounds on the number of colors for more generalized constrained bipartite edge coloring problems can be found in =-=[14]-=-. Using the coloring algorithm presented in [24] for ff = 4=3 as a subroutine, the wavelength routing algorithm maintains at each phase the following two invariants: I. The total number of colors is n... |

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Citation Context ...ts about optimal and nearly--optimal bandwidth utilization in all--pairs and down conversion trees. All results make use of the expansion properties of Ramanujan graphs. The interested reader may see =-=[3, 6, 19]-=- for a complete discussion and proofs. Gargano [19] and independently Auletta et al. [6] (see also [3]) show that using Ramanujan graphs of constant degree, we can achieve optimal bandwidth utilizatio... |

2 |
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