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32
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 84 (20 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 30 (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.
The Complexity of Path Coloring and Call Scheduling
 Theoretical Computer Science
, 2000
"... Modern highperformance communication networks pose a number of challenging problems concerning the efficient allocation of resources to connection requests. In alloptical networks with wavelengthdivision multiplexing, connection requests must be assigned paths and colors (wavelengths) such that i ..."
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Cited by 28 (5 self)
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Modern highperformance communication networks pose a number of challenging problems concerning the efficient allocation of resources to connection requests. In alloptical networks with wavelengthdivision multiplexing, connection requests must be assigned paths and colors (wavelengths) such that intersecting paths receive different colors, and the goal is to minimize the number of colors used. This path coloring problem is proved NPhard for undirected and bidirected ring networks. Path coloring in undirected tree networks is shown to be equivalent to edge coloring of multigraphs, which implies a polynomialtime optimal algorithm for trees of constant degree as well as NPhardness and an approximation algorithm with absolute approximation ratio 4:3 and asymptotic approximation ratio 1:1 for trees of arbitrary degree. For bidirected trees, path coloring is shown to be NPhard even in the binary case. A polynomialtime optimal algorithm is given for path coloring in undirected or bidir...
On the Wavelength Assignment Problem in Multifiber WDM Star and Ring Networks
 IEEE Infocom
, 2000
"... This paper studies the offline wavelength assignment problem in star and ring networks that deploy multiple fibers between nodes and use Wavelength Division Multiplexing (WDM) for transmission. The results in this paper show that the ability to switch between fibers increases wavelength utilization ..."
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Cited by 27 (1 self)
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This paper studies the offline wavelength assignment problem in star and ring networks that deploy multiple fibers between nodes and use Wavelength Division Multiplexing (WDM) for transmission. The results in this paper show that the ability to switch between fibers increases wavelength utilization. In particular, sharper perfiber bounds on the number of required wavelengths are derived for the multifiber version of the assignment problem in star and ring networks. Additionally, the complexity of the problem is studied and several constrained versions of the problem are also considered for star and ring networks. A summary of contributions is provided in the first section. 1 Introduction Optical networks hold out the promise of meeting the high transmission quality and large bandwidth desired by enduser applications. Among various transmission technologies for optical networks, Wavelength Division Multiplexing (WDM), because of its efficient use of bandwidth, has received consider...
Wavelength Assignment Problem on AllOptical Networks with k Fibres per Link
, 2000
"... Given a (possibly directed) network, the wavelength assignment problem is to minimize the number of wavelengths that must be assigned to communication paths so that paths sharing an edge are assigned different wavelengths. Our generalization to multigraphs with k parallel edges for each link (k ..."
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Cited by 21 (1 self)
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Given a (possibly directed) network, the wavelength assignment problem is to minimize the number of wavelengths that must be assigned to communication paths so that paths sharing an edge are assigned different wavelengths. Our generalization to multigraphs with k parallel edges for each link (k fibres per link, with switches at nodes) may be of practical interest. While the wavelength assignment problem is NPhard, even for a single fibre, and even in the case of simple network topologies such as rings and trees, the new model suggests many nice combinatorial problems, some of which we solve. For example, we show that for many network topologies, such as rings, stars, and specific trees, the number of wavelengths needed in the kfibre model is less than 1/k fraction of the number required for a single fibre. We also study the existence and behavior of a gap between the minimum number of wavelengths and the natural lower bound of network congestion, the maximum number of...
The Maximum EdgeDisjoint Paths Problem In Bidirected Trees
 SIAM Journal on Discrete Mathematics
, 1998
"... . A bidirected tree is the directed graph obtained from an undirected tree by replacing each undirected edge by two directed edges with opposite directions. Given a set of directed paths in a bidirected tree, the goal of the maximum edgedisjoint paths problem is to select a maximumcardinality subse ..."
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Cited by 18 (4 self)
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. A bidirected tree is the directed graph obtained from an undirected tree by replacing each undirected edge by two directed edges with opposite directions. Given a set of directed paths in a bidirected tree, the goal of the maximum edgedisjoint paths problem is to select a maximumcardinality subset of the paths such that the selected paths are edgedisjoint. This problem can be solved optimally in polynomial time for bidirected trees of constant degree, but is MAXSNPhard for bidirected trees of arbitrary degree. For every fixed " ? 0, a polynomialtime (5=3+ ")approximation algorithm is presented. Key words. approximation algorithms, edgedisjoint paths, bidirected trees AMS subject classifications. 68Q25, 68R10 1. Introduction. Research on disjoint paths problems in graphs has a long history [12]. In recent years, edgedisjoint paths problems have been brought into the focus of attention by advances in the field of communication networks. Many modern network architectures estab...
Randomized Path Coloring on Binary Trees
 3rd International Workshop on Approximation ALgorihms for Combinatorial Optimization Problems (APPROX’00), Vol.1913
, 2000
"... . Motivated by the problem of WDM routing in alloptical networks, we study the following NPhard problem. We are given a directed binary tree T and a set R of directed paths on T . We wish to assign colors to paths in R, in such a way that no two paths that share a directed arc of T are assig ..."
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Cited by 16 (5 self)
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. Motivated by the problem of WDM routing in alloptical networks, we study the following NPhard problem. We are given a directed binary tree T and a set R of directed paths on T . We wish to assign colors to paths in R, in such a way that no two paths that share a directed arc of T are assigned the same color and that the total number of colors used is minimized. Our results are expressed in terms of the depth of the tree and the maximum load l of R, i.e., the maximum number of paths that go through a directed arc of T . So far, only deterministic greedy algorithms have been presented for the problem. The best known algorithm colors any set R of maximum load l using at most 5l=3 colors. Alternatively, we say that this algorithm has performance ratio 5=3. It is also known that no deterministic greedy algorithm can achieve a performance ratio better than 5=3. In this paper we define the class of greedy algorithms that use randomization. We study their limitations and pr...
OffLine and OnLine CallScheduling in Stars and Trees
 in Proceedings of the 23rd International Workshop on GraphTheoretic Concepts in Computer Science, WG ‘97, LNCS1335, SpringerVerlag
, 1997
"... . Given a communication network and a set of call requests, the goal is to find a minimum makespan schedule for the calls such that the sum of the bandwidth requirements of simultaneously active calls using the same link does not exceed the capacity of that link. In this paper the callschedulin ..."
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Cited by 12 (2 self)
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. Given a communication network and a set of call requests, the goal is to find a minimum makespan schedule for the calls such that the sum of the bandwidth requirements of simultaneously active calls using the same link does not exceed the capacity of that link. In this paper the callscheduling problem is studied for star and tree networks. Lower and upper bounds on the worstcase performance of ListScheduling (LS) and variants of it are obtained for callscheduling with arbitrary bandwidth requirements and either unit call durations or arbitrary call durations. LS does not require advance knowledge of call durations and, hence, is an online algorithm. It has performance ratio (competitive ratio) at most 5 in star networks. A variant of LS for calls with unit durations is shown to have performance ratio at most 2 2 3 . In tree networks with n nodes, a variant of LS for calls with unit durations has performance ratio at most 6, and a variant for calls with arbitrary d...