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28
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 (6 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.
Resource Allocation Problems in Multifiber WDM Tree Networks
, 2003
"... Alloptical networks with multiple fibers lead to several interesting optimization problems. In this paper, we consider the problem of minimizing the total number of fibers necessary to establish a given set of requests with a bounded number w of wavelengths, and the problem of maximizing the num ..."
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Cited by 19 (8 self)
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Alloptical networks with multiple fibers lead to several interesting optimization problems. In this paper, we consider the problem of minimizing the total number of fibers necessary to establish a given set of requests with a bounded number w of wavelengths, and the problem of maximizing the number of accepted requests for given fibers and bounded number w of wavelengths. We study both problems in undirected tree networks T = (V, E) and present approximation algorithms with ratio 1 + 4E log V /OPT and 4 for the former and with ratio 2.542 for the latter.
Approximation Algorithms and Complexity Results for Path Problems in Trees of Rings
, 2001
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Minimizing Request Blocking in AllOptical Rings
 In Proc. INFOCOM 2003
, 2003
"... In alloptical networks that use WDM technology it is often the case that several communication requests have to be blocked, due to bandwidth and technology limitations. Minimizing request blocking is therefore an important task calling for algorithmic techniques for efficient routing and wavelength ..."
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Cited by 12 (4 self)
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In alloptical networks that use WDM technology it is often the case that several communication requests have to be blocked, due to bandwidth and technology limitations. Minimizing request blocking is therefore an important task calling for algorithmic techniques for efficient routing and wavelength assignment.
2006), Complexity of wavelength assignment in optical network optimization
 in Proceedings of IEEE INFOCOM
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Wavelength management in WDM rings to maximize the number of connections
 In 24th International Symposium on Theoretical Aspects of Computer Science (STACS 07), volume LNCS 4393
, 2007
"... Abstract. We study computationally hard combinatorial problems arising from the important engineering question of how to maximize the number of connections that can be simultaneously served in a WDM optical network. In such networks, WDM technology can satisfy a set of connections by computing a rou ..."
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Cited by 8 (3 self)
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Abstract. We study computationally hard combinatorial problems arising from the important engineering question of how to maximize the number of connections that can be simultaneously served in a WDM optical network. In such networks, WDM technology can satisfy a set of connections by computing a route and assigning a wavelength to each connection so that no two connections routed through the same fiber are assigned the same wavelength. Each fiber supports a limited number of w wavelengths and in order to fully exploit the parallelism provided by the technology, one should select a set connections of maximum cardinality which can be satisfied using the available wavelengths. This is known as the maximum routing and path coloring problem (maxRPC). Our main contribution is a general analysis method for a class of iterative algorithms for a more general coloring problem. A lower bound on the benefit of such an algorithm in terms of the optimal benefit and the number of available wavelengths is given by a benefitrevealing linear program. We apply this method to maxRPC in both undirected and bidirected rings to obtain bounds on the approximability of several algorithms. Our results also apply to the problem maxPC where paths instead of connections are given as part of the input. We also study the profit version of maxPC in rings where each path has a profit and the objective is to satisfy a set of paths of maximum total profit.
A BIASED RANDOMKEY GENETIC ALGORITHM FOR ROUTING AND WAVELENGTH ASSIGNMENT
, 2010
"... The problem of routing and wavelength assignment (RWA) in wavelength division multiplexing (WDM) optical networks consists in routing a set of lightpaths and assigning a wavelength to each of them, such that lightpaths whose routes share a common fiber are assigned different wavelengths. This probl ..."
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Cited by 7 (3 self)
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The problem of routing and wavelength assignment (RWA) in wavelength division multiplexing (WDM) optical networks consists in routing a set of lightpaths and assigning a wavelength to each of them, such that lightpaths whose routes share a common fiber are assigned different wavelengths. This problem was shown to be NPhard when the objective is to minimize the total number of wavelengths used. We propose a genetic algorithm with random keys for routing and wavelength assignment with the goal of minimizing the number of different wavelengths used in the assignment. This algorithm extends the best heuristic in the literature by embedding it into an evolutionary framework. Computational results show that the new heuristic improves the stateoftheart algorithms in the literature.
Fractional and Integral Coloring of LocallySymmetric Sets of Paths on Binary Trees
, 2003
"... Motivated by the problem of allocating optical bandwidth in treeshaped WDM networks, we study the fractional path coloring problem in trees. We consider the class of locallysymmetric sets of paths on binary trees and prove that any such set of paths has a fractional coloring of cost at most 1 ..."
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Cited by 3 (1 self)
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Motivated by the problem of allocating optical bandwidth in treeshaped WDM networks, we study the fractional path coloring problem in trees. We consider the class of locallysymmetric sets of paths on binary trees and prove that any such set of paths has a fractional coloring of cost at most 1:367L, where L denotes the load of the set of paths. Using this result, we obtain a randomized algorithm that colors any locallysymmetric set of paths of load L on a binary tree (with reasonable restrictions on its depth) using at most 1:367L + o(L) colors, with high probability.
Routing in AllOptical Ring Networks Revisited
, 2004
"... A common approach for establishing connection requests in an optical ring network that uses wavelengthdivision multiplexing is to first find a routing of the requests that minimizes the congestion and then deal with the wavelength allocation. The congestion of a routing, however, does not reflect it ..."
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Cited by 3 (1 self)
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A common approach for establishing connection requests in an optical ring network that uses wavelengthdivision multiplexing is to first find a routing of the requests that minimizes the congestion and then deal with the wavelength allocation. The congestion of a routing, however, does not reflect its wavelength requirements. Indeed, we observe that for certain instances such an approach can result in considerable waste of network resources. To overcome this, we propose a new routing objective, namely to minimize the maximum clique of the routing, i.e., the maximum number of connections that pairwise share a common fiber. We present optimal algorithms and heuristics for finding minimum clique routings and perform experiments to evaluate their performance.
Packet Routing: Complexity and Algorithms
"... Storeandforward packet routing belongs to the most fundamental tasks in network optimization. Limited bandwidth requires that some packets cannot move to their destination directly but need to wait at intermediate nodes on their path or take detours. In particular, for time critical applications, ..."
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Storeandforward packet routing belongs to the most fundamental tasks in network optimization. Limited bandwidth requires that some packets cannot move to their destination directly but need to wait at intermediate nodes on their path or take detours. In particular, for time critical applications, it is desirable to find schedules that ensure fast delivery of the packets. It is thus a natural objective to minimize the makespan, i.e., the time at which the last packet arrives at its destination. In this paper we present several new ideas and techniques that lead to novel algorithms and hardness results.