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Graph problems arising from wavelengthrouting in alloptical networks
, 1997
"... We survey the theoretical results obtained for wavelength routing in all–optical networks, present some new results and propose several open problems. In all–optical networks the vast bandwidth available is utilized through wavelength division multiplexing: a single physical optical link can carry s ..."
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Cited by 81 (21 self)
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We survey the theoretical results obtained for wavelength routing in all–optical networks, present some new results and propose several open problems. In all–optical networks the vast bandwidth available is utilized through wavelength division multiplexing: a single physical optical link can carry several logical signals, provided that they are transmitted on different wavelengths. The information, once transmitted as light, reaches its destination without being converted to electronic form in between, thus reaching high data transmission rates. We consider both networks with arbitrary topologies and particular networks of practical interest.
AlltoAll Communication for some WavelengthRouted AllOptical Networks
, 1998
"... This paper studies the problem of AlltoAll Communication for optical networks. In such networks the vast bandwidth available is utilized through wavelength division multiplexing (WDM): a single physical optical link can carry several logical signals, provided that they are transmitted on different ..."
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Cited by 28 (1 self)
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This paper studies the problem of AlltoAll Communication for optical networks. In such networks the vast bandwidth available is utilized through wavelength division multiplexing (WDM): a single physical optical link can carry several logical signals, provided that they are transmitted on different wavelengths. In this paper we consider alloptical (or singlehop) networks, where the information, once transmitted as light, reaches its destination without being converted to electronic form in between, thus reaching high data transmission rates. In this model, we give optimal alltoall protocols, using minimum numbers of wavelengths, for particular networks of practical interest, namely the ddimensional square tori with even side, the corresponding meshes and the Cartesian sums of complete graphs.
Efficient Wavelength Routing on Directed Fiber Trees
, 1996
"... . We address the issue of efficiently assigning wavelengths to communication requests in wavelength division multiplexing (WDM) optical networks. We consider directed tree and tree of rings topologies. These are topologies of concrete practical relevance for which undirected underlying graph models ..."
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Cited by 24 (11 self)
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. We address the issue of efficiently assigning wavelengths to communication requests in wavelength division multiplexing (WDM) optical networks. We consider directed tree and tree of rings topologies. These are topologies of concrete practical relevance for which undirected underlying graph models have been studied by Raghavan and Upfal [6]. Directed models were first studied by Mihail et al [4]. For trees, we give a polynomial time routing algorithm that, for requests of maximum load L per directed fiber link, uses at most 7=4L wavelengths. This improves the bound of Mihail et al.. As a corollary we also give an algorithm for trees of rings that uses 7=2L wavelengths. 1 Introduction Optics is a major technology that drives very high speed networking to the future. A single optical wavelength supports rates of gigabitspersecond (which in turn support multiple channels of voice, data, and video [3] [5]). Multiple laser beams that are propagated over the same fiber on distinct optica...
Fractional Path Coloring with Applications to WDM Networks
, 2001
"... This paper addresses the natural relaxation of the path coloring problem, in which one needs to color directed paths on a symmetric directed graph with a minimum number of colors, in such a way that paths using the same arc of the graph have different colors. This classic combinatorial problem finds ..."
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Cited by 20 (5 self)
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This paper addresses the natural relaxation of the path coloring problem, in which one needs to color directed paths on a symmetric directed graph with a minimum number of colors, in such a way that paths using the same arc of the graph have different colors. This classic combinatorial problem finds applications in the minimization of the number of wavelengths in wavelength division multiplexing (WDM) alloptical networks.
Multicast Routing and Wavelength Assignment in Multihop Optical Networks
 IEEE/ACM Transactions on Networking
, 2002
"... Abstract. This paper addresses multicast routing in multihop optical networks employing wavelengthdivision multiplexing (WDM). We consider a model in which multicast communication requests are made and released dynamically over time. A multicast connection is realized by constructing a multicast t ..."
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Cited by 14 (2 self)
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Abstract. This paper addresses multicast routing in multihop optical networks employing wavelengthdivision multiplexing (WDM). We consider a model in which multicast communication requests are made and released dynamically over time. A multicast connection is realized by constructing a multicast tree which distributes the message from the source node to all destination nodes such that the wavelengths used on each link and the receivers and transmitters used at each node are not used by existing circuits. We show that although the routing and wavelength assignment in this model is NPcomplete, the wavelength assignment problem can be solved in linear time. 1
A Note on Optical Routing on Trees
, 1997
"... Bandwidth is a very valuable resource in wavelength division multiplexed optical networks. The problem of finding an optimal assignment of wavelengths to requests is of fundamental importance in bandwidth utilization. We present a polynomialtime algorithm for this problem on fixed constantsize topo ..."
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Cited by 14 (0 self)
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Bandwidth is a very valuable resource in wavelength division multiplexed optical networks. The problem of finding an optimal assignment of wavelengths to requests is of fundamental importance in bandwidth utilization. We present a polynomialtime algorithm for this problem on fixed constantsize topologies. We combine this algorithm with ideas from Raghavan and Upfal [15] to obtain an optimal assignment of wavelengths on constant degree undirected trees. Mihail, Kaklamanis, and Rao [14] posed the following open question: what is the complexity of this problem on directed trees? We show that it is NPcomplete both on binary and constant depth directed trees. Keywords: Algorithms, Combinatorial Problems, Computational Complexity, Interconnection Networks. 1 Introduction Motivation. Developments in fiberoptic networking technology using Wavelength Division Multiplexing (WDM) have finally reached the point where it 1 Supported by ONR Young Investigator Award N000149310590. This work ...
Sparse and Limited Wavelength Conversion in AllOptical Tree Networks
, 2000
"... We study the problem of assigning a minimum number of colors to directed paths (dipaths) of a tree, so that any two dipaths that share a directed edge of the tree are not assigned the same color. The problem has applications to wavelength routing in WDM alloptical tree networks, an important engine ..."
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Cited by 13 (0 self)
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We study the problem of assigning a minimum number of colors to directed paths (dipaths) of a tree, so that any two dipaths that share a directed edge of the tree are not assigned the same color. The problem has applications to wavelength routing in WDM alloptical tree networks, an important engineering problem. Dipaths represent communication requests, while colors correspond to wavelengths that must be assigned to requests so that multiple users can communicate simultaneously through the same optical fiber. Recent work on wavelength routing in trees has studied a special class of algorithms which are called greedy. Although these algorithms are simple and implementable in a distributed setting, it has been proved that there are cases where a bandwidth utilization of 100% is not possible. Thus, in this work, we relax the constraints of the original engineering problem and use devices called wavelength converters that are able to convert the wavelength a...
Directed Virtual Path Layouts in ATM Networks
, 1999
"... Motivated by Asynchronous Transfer Mode (ATM) in telecommunication networks, we investigate the problem of designing a directed virtual topology on a directed physical topology, which consists in finding a set of directed virtual paths (VPs) satisfying some constraints in terms of load (the number o ..."
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Cited by 11 (5 self)
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Motivated by Asynchronous Transfer Mode (ATM) in telecommunication networks, we investigate the problem of designing a directed virtual topology on a directed physical topology, which consists in finding a set of directed virtual paths (VPs) satisfying some constraints in terms of load (the number of VPs sharing a physical link) and hop count (the number of VPs used to establish a connection). For both general and particular networks, such as paths, cycles, meshes, tori and trees, we derive tight bounds on the virtual diameter (the maximum hop count for a connection) as a function of the network capacity (the maximum load of a physical link).
Routing In AllOptical Networks: Algorithmic And GraphTheoretic Problems
 Information and Complexity
, 2000
"... : This paper surveys theoretical results for wavelengthrouting in all optical networks and presents several open problems. We focus our attention on graphtheoretical problems and proof techniques. 1 INTRODUCTION Optical networks are emerging as key technology in communication networks and are ..."
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Cited by 10 (2 self)
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: This paper surveys theoretical results for wavelengthrouting in all optical networks and presents several open problems. We focus our attention on graphtheoretical problems and proof techniques. 1 INTRODUCTION Optical networks are emerging as key technology in communication networks and are expected to dominate many applications, such as video conferencing, scientific visualisation, realtime medical imaging, highspeed supercomputing and distributed computing [18, 19, 33, 36]. The books of Green [18] and McAulay [30] offer a comprehensive overview of the physical theory and applications of this emerging technology. In WDM (Wavelength Division Multiplexing) optical networks, the bandwidth available in optical fiber is utilised by partitioning it into several channels, each at a different wavelength. Each wavelength can carry a separate stream of data. In general, a WDM network consists of routing nodes interconnected by pointtopoint unidirectional optic fiber links. Each...