Routing and path multicoloring

Nomikos, Christos; Pagourtzis, Aris; Zachos, Stathis

doi:10.1016/s0020-0190(01)00167-3

Cited by 30 publications

(15 citation statements)

References 12 publications

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“…MINFIBCOST-RPMC in rings is NP-hard, since the problern with uniform costs, which is a special case, is NP-hard [9]; the same holds for MINFIBCOST-PMC in rings. MINWAv-RPMC in rings, stars and spiders is also NP-hard (since it is a generalization of the classical routing and path colaring problern which is NP-hard for such topologies [11]); this is also true for MINWAv-PMC in rings as well as for the directed version of both problems in rings.…”

Section: Lntroductionmentioning

confidence: 91%

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Fiber Cost Reduction and Wavelength Minimization in Multifiber WDM Networks

Nomikos

Pagourtzis

Potika

et al. 2004

Lecture Notes in Computer Science

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Abstract. Motivated by the increasing importance of multifiber WDM networks we study two routing and wavelength assignment problems in such networks:Fiber Cast Minimization: the number of wavelengths per fiber is given and we want to minimize the cost of fiber links that need to be reserved in order to satisfy a set of communication requests; we introduce a generalized setting where network pricing is nonuniform, that is the cost of hiring a fiber may differ from link to link. W avelength Minimization: the number of available parallel fibers on each link is given and we want to minimize the wavelengths per fiber that are needed in order to satisfy a set of communication requests. For each problern we consider two variations: undirected, which corresponds to full-duplex communication, and directed, which corresponds to one-way communication. Moreover, for rings we also study the problern in the case of pre-determined routing. We present exact or constant-ratio approximation algorithms for all the above variations in chain, ring, star and spider networks. lntroductionAll-optical networks make it possible to transmit data at very high speed. The technology that enables transmitting more than one signal along a single optical fiber is called Wavelength Division Multiplexing (WDM); many signals can be simultaneously carried over the same physical link by light beams of different wavelengths. Recent developments make it possible to use multiple fibers on each link, allowing any signal to switch fiber at any node; however, it is preferred for each signal to remain on the same wavelength from t ransmitter to receiver, in order to avoid wavelength conversion.A multifiber network can be described by a graph G = (V, E) and a function fJ-: E ---+ lN that defines the multiplicity of fibers on each link. The set of requests R is a set of pair of nodes. A routing and path multicoloring 1 for n ( w .r. t. fJ-( e)) 1 Color collisions between paths that use the same edge are allowed , so we use the term "path multicoloring", as opposed to classical "path coloring" where paths that share an edge must receive different colors.

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Section: Lntroductionmentioning

confidence: 91%

“…The problern of minimizing the number of active fibers in multifiber networks with uniform fiber costs was introduced in [9], where polynomial-time solvability was shown for chains and 2-approximation algorithms were given for the undirected problern in ring and star networks. Their results for chains and stars extend to MINFIBCOST-RPMC.…”

Section: Related Workmentioning

confidence: 99%

Fiber Cost Reduction and Wavelength Minimization in Multifiber WDM Networks

Nomikos

Pagourtzis

Potika

et al. 2004

Lecture Notes in Computer Science

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“…As noticed in [4] this problem is NP-hard in general graphs, in fact even in rings and stars. Therefore, it is also NP-hard to compute an optimal Nash Equilibrium even in the case of rings and stars.…”

Section: Theorem 1 For Any Game G P W In S-pmcmentioning

confidence: 95%

“…However, we show that there exists an efficient algorithm that computes optimal Nash Equilibria for a subclass of S-PMC(Tree). Furthermore, we show that we can use a known algorithm for Path MultiColoring in stars [4] to compute approximate Nash Equilibria for S-PMC(Star) games. We will only state the theorems and omit the proofs.…”

Section: Theorem 1 For Any Game G P W In S-pmcmentioning

confidence: 99%

“…To this end, several optimization problems have been defined and studied, the objective being to minimize either the maximum fiber multiplicity per edge [1,2,3] or the sum of these maximum multiplicities over all edges of the graph [4,5,6]; in another scenario the allowed fiber multiplicity per edge is given and the goal is to minimize the number of wavelengths needed [7,8,5].…”

Section: Introductionmentioning

confidence: 99%

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On a Non-cooperative Model for Wavelength Assignment in Multifiber Optical Networks

Bampas

Pagourtzis

Pierrakos

et al. 2008

Algorithms and Computation

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Abstract. We study path multicoloring games that describe situations in which selfish entities possess communication requests in a multifiber all-optical network. Each player is charged according to the maximum fiber multiplicity that her color (wavelength) choice incurs and the social cost is the maximum player cost. We investigate the price of anarchy of such games and provide two different upper bounds for general graphsnamely the number of wavelengths and the minimum length of a path of maximum disutility, over all worst-case Nash Equilibria-as well as matching lower bounds which hold even for trees; as a corollary we obtain that the price of anarchy in stars is exactly 2. We also prove constant bounds for the price of anarchy in chains and rings in which the number of wavelengths is relatively small compared to the load of the network; in the opposite case we show that the price of anarchy is unbounded.

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Wavelength assignment in multifiber star networks

Bian

2010

Networks

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We consider the wavelength assignment problem in WDM optical networks with multiple parallel fibers: Given a set P of paths, assign a color to each path such that the number of paths with the same color containing any link is at most the number of fibers in the link. Assuming the number of fibers in each link is fixed, we study two optimization problems. One is to minimize the number of colors for coloring P . The other is to color as many paths of P as possible with a given number of colors. We show that both the minimization and the maximization problems are NP-hard in star networks with a uniform odd number of fibers. We give polynomial time optimal algorithms for the minimization and maximization problems in star networks with an even number of fibers and in the generalized star networks with a uniform even number of fibers. We also give a 1.58-approximation algorithm for the maximization problem in the generalized star networks with an arbitrary number of fibers. The algorithms for the maximization problem in the generalized stars are based on our newly developed algorithm, which optimally solves the call control problem in the generalized star networks. The call control algorithm is of independent interest.

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Routing and path multicoloring

Cited by 30 publications

References 12 publications

Fiber Cost Reduction and Wavelength Minimization in Multifiber WDM Networks

Fiber Cost Reduction and Wavelength Minimization in Multifiber WDM Networks

On a Non-cooperative Model for Wavelength Assignment in Multifiber Optical Networks

Wavelength assignment in multifiber star networks

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