Y. Bartal and S. Leonardi. On-line routing in all-optical networks. In Proceedings of the 24th International Colloquium on Automata, Languages and Programming ICALP '97, LNCS 1256, pages 516--526. Springer-Verlag, 1997.  Home/Search   Document Details and Download   Summary   Related Articles   Check

.... of randomized on line algorithms against oblivious adversaries, i.e. we assume that input instances may not be dependent on the random choices of the algorithm (although they may depend on the probability distribution using which the random choices of the algorithm are made) Bartal and Leonardi [5] reduce the on line path coloring problem in trees to the on line coloring of d inductive graphs. A graph called d inductive if its vertices can be numbered in such a way that each vertex has at most d adjacent vertices with higher numbers. Irani in [20] gives an on line algorithm for coloring a ....

....graphs. A graph called d inductive if its vertices can be numbered in such a way that each vertex has at most d adjacent vertices with higher numbers. Irani in [20] gives an on line algorithm for coloring a d inductive graph with n vertices using at most O(d logn) colors. Bartal and Leonardi [5] observed that the con ict graph de ned by the paths in an instance of the path coloring problem on a tree is 2(C 1) inductive, where C is the clique number of the con ict graph. Note that any algorithm requires at least C colors to color an instance whose con ict graph has a clique of size C ....

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Y. Bartal and S. Leonardi. On-Line Routing in All-Optical Networks, Theoretical Computer Science Vol. 221(1-2), 1999, pp. 19-39.

....the performance of algorithms using certain statistical models or simulation models of network tra#c [21, 2, 14] But in recent years, we have seen a trend of research that does not make any such assumptions. In particular, a lot of recent work in WDM networks is based on the maximum load model [20, 19, 11, 9, 4, 1]. In the maximum load model, the route of each request is given. The problem is to find the minimum number of wavelengths to satisfy a given request sequence characterized by a maximum load, which is the maximum number of lightpaths over any link in the network. The maximum load model is ....

Yair Bartal and Stefano Leonardi. On-line routing in alloptical networks. In Pierpaolo Degano, Robert Gorrieri, and Alberto Marchetti-Spaccamela, editors, Automata, Languages and Programming, 24th International Colloquium, volume 1256 of Lecture Notes in Computer Science, pages 516--526, Bologna, Italy, 7--11 July 1997. Springer-Verlag.

....instances and permutation instances. The on line version of the undirected path coloring problem (where the connection requests are given to the algorithm one by one, and colors and paths must be assigned immediately without knowledge of future requests) was studied by Bartal and Leonardi [3]. They obtained deterministic on line algorithms with 6 competitive ratio O(log n) for networks with n nodes whose topology is that of a tree, a tree of rings, or a mesh. In addition, they presented a matching lower bound of 16 n) for all on line algorithms for undirected path coloring in ....

Y. Bartal and S. Leonardi. On-line routing in all-optical networks. In Proceedings of the 24th International Colloquium on Automata, Languages and Programming ICALP '97, LNCS 1256, pages 516-526. Springer-Verlag, 1997.

....bounded by a constant [5, 6] The directed version is NP hard already for binary trees [6] In the on line version of the wavelength allocation problem the algorithm is given requests one by one and must assign wavelengths immediately without knowledge about future requests. Bartal and Leonardi [3] obtain deterministic on line algorithms with competitive ratio O(log n) for networks with n processors whose topology is that of a tree, a tree of rings, or a mesh. In addition, they present a matching lower bound of Omega (log n) for all on line algorithms for wavelength allocation in meshes, ....

....bound of Omega ( log n log log n ) for trees. Note that the on line version of the wavelength allocation problem corresponds to a call scheduling problem where the algorithm must assign starting times to call requests one by one before the first call is established. Hence, the lower bounds in [3] do not apply to the call scheduling problem we study in this paper. Furthermore, their algorithms work for the call scheduling problem only in the case of unit durations and unit bandwidths. Scheduling File Transfers. Coffman et al. study a file transfer scheduling problem that corresponds to ....

Y. Bartal and S. Leonardi. On-line routing in all-optical networks. In Proceedings of the 24th International Colloquium on Automata, Languages and Programming ICALP '97, LNCS 1256, pages 516--526. Springer-Verlag, 1997.

....The colors correspond to wavelengths in optic ber links. The goal is to minimize the number of colors used. Bartal, Fiat, and Leonardi [5] provided lower bounds for the path coloring and many other related problems. On line algorithms in the cost model have been studied by Bartal and Leonardi [7]. In particular, they provided an O(log N) competitive deterministic on line algorithm (which is not distributed) as well as a matching ng N) lower bound for this problem on N node meshes. As the congestion in the routing problem is a lower bound for the number of colors used in the path ....

....that are assigned to s i s in Part P1 can be routed down then right to the corresponding nodes on T r 1 T (r 1) that are assigned to t i s in Path P2. It is simple to see that the paths are edge disjoint. Theorem 1 follows immediately by Lemmas 1 and 2. Now consider the the path coloring problem [7] in an on line and distributed setting. In this problem we must color the paths assigned in the on line source routing problem studied in our paper such that any tow packets that share an edge have di erent colors. Note that the congestion is a lower bound for the number of colors used in the path ....

Y. Bartal and S. Leonardi. On-line routing in all-optical networks. Theoretical Computer Science, 221:19-39, 1999.

....9. 4] If OPT , then there exists fi = O(log n) such that the routing algorithm never fails. Thus, the load on a link never exceeds fi . It is possible to translate the Omega (log n) lower bound for restricted assignment to the virtual circuit routing problem on directed graphs. Recently [15] showed that the lower bounds hold also for undirected graphs. 9 Competitive ratio Identical 2 Gamma ffl Related Theta(1) Restricted Theta(log n) Unrelated Theta(log n) Routing Theta(log n) Fig. 1. Summary of competitive ratio for permanent tasks 4 Temporary tasks unknown duration ....

Y. Bartal and S. Leonardi. On-line routing in all-optical networks. In Proc. 24rd International Colloquium on Automata, Languages, and Programming, 1997.

....that if S is the set of all paths on T then L S = WS . Moreover, the equality LS = WS holds for every S if and only if T has at most one node of degree larger than 2 [17] The determination of W S is NP hard [16] and it is known that there are instances for which W S =LS 5=4 [25] Several authors [25, 24, 23, 9] have considered the problem of designing algorithms for minimizing the number of wavelengths used to route a set of requests of load L S , the best bound known is 5L S =3. Therefore, if a dipath must employ the same wavelength on each of its links then it is possible to accommodate only requests ....

....is a strong function of the input and output wavelengths, thus leading to limited conversion capability [33] Different types of conversion are illustrated in Figure 1. 1. 2 Related Work Much work has been recently devoted to the problem of routing in all optical networks, see for example [1, 6, 7, 8, 13, 16, 9, 32, 33]. A survey of graph theoretic problems associated with routing in optical networks can be found in [11] Routing in all optical tree like networks has also received much attention [29, 23, 25, 17] A good deal of work has been recently devoted to WDM routing with converters, see for example [18, ....

Y. Bartal, S. Leonardi, "On--Line Routing in All-Optical Networks", Proceedings of 24th International Colloquium on Automata, Languages, and Programming (ICALP 97), Bologna, Italy, July 1997.

No context found.

Y. Bartal and S. Leonardi. On-line routing in all-optical networks. In Proc. of the 24th International Colloqium on Automata, Languages and Programming, Springer Verlag LNCS 1256, pages 516--526, 1997.

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Y. Bartal and S. Leonardi, On-line routing in all-optical networks, in Proceedings of the 24th International Colloquium on Automata, Languages, and Programming, Lecture Notes in Comput. Sci. 1256, Springer, Berlin, 1997, pp. 516--526.

No context found.

Y. Bartal and S. Leonardi. On-line routing in all-optical networks. In Proceedings of the 24th International Colloqium on Automata, Languages and Programming, LNCS 1256, pages 516--526. Springer-Verlag, 1997.

No context found.

Yair Bartal and Stefano Leonardi. On-line routing in all-optical networks. In Proc. 24th International Colloquium on Automata, Languages, and Programming, volume 1256 of Lecture Notes in Computer Science, pages 516--526. Springer, 1997.

....the intersection graph, is in this case associated with a path on a tree network. Two vertices are adjacent in the graph if the two corresponding paths are intersecting. This problem has recently received a growing attention due to its application to wavelength assignment in optical networks [RU94,BL97,GSR96] Several authors show an O( Delta) competitive deterministic algorithm for the problem of coloring online paths on a tree network (see for instance [BL97,GSR96] where Delta is the diameter of the graph. Bartal and Leonardi [BL97] also show an almost matching Omega ( Delta= log ....

.... This problem has recently received a growing attention due to its application to wavelength assignment in optical networks [RU94,BL97,GSR96] Several authors show an O( Delta) competitive deterministic algorithm for the problem of coloring online paths on a tree network (see for instance [BL97,GSR96] where Delta is the diameter of the graph. Bartal and Leonardi [BL97] also show an almost matching Omega ( Delta= log Delta) deterministic lower bound on a tree of diameter Delta = O(log n) where n is the number of vertices of the graph. In this paper we present the first ....

[Article contains additional citation context not shown here]

Y. Bartal and S. Leonardi. On-line routing in all-optical networks. In Proceedings of the 24th International Colloqium on Automata, Languages and Programming, LNCS 1256, pages 516--526. Springer-Verlag, 1997.

....ratio. Later we study the problem on meshes: ffl We present an optimal O(log n) competitive algorithm for meshes that obtains a constant fraction of the expectation with probability that tends to 1, as OPT log 4 n tends to infinity. This algorithm is based on some of the ideas of [KT95] and [BL97] and on new ideas presented here. Beyond our results on this specific set of problems, we hope that this work could be a first step towards understanding the relationship between competitiveness and the concentration of the solution around the expected benefit for on line randomized algorithms ....

....from this abstract. For the second part of the claim we consider an intesection graph of paths on a tree. Our claim follows from the fact that if each edge in the tree is included in at most g of these paths, then the intersection graph is a (2(g Gamma 1) inductive graph (this is proved in [BL97]) 5 Since the capacity used by the AAP algorithm is log 4D, any edge is used by at most log 4D calls, and the number of intersections is bounded by jC(oe)j Delta 2(log 4D Gamma 1) jC(oe)j Delta 2 log 2D. 2 The randomized selection procedure used in conjunction with this filter is the same ....

[Article contains additional citation context not shown here]

Y. Bartal and S. Leonardi. On-line Routing in All-Optical Networks. To appear in Proc. of ICALP '97.

....class of planar graphs, where n is the number of nodes in the network. Rabani [R96] improved the result for meshes to O(poly(log log n) The path coloring problem has also been studied in its on line version. Algorithms with an O(log n) competitive ratio have been devised by Bartal and Leonardi [BL96] for trees, trees of rings and meshes; Gerstel, Sasaki and Ramaswami consider the problem on rings and trees, and give O(log n) competitive algorithms [GSR96] Bartal and Leonardi also present an Omega Gamma log n log log n ) lower bound for trees and an Omega Gamma 26 n) lower bound for ....

Y. Bartal and S. Leonardi. On-line routing in all-optical networks. Manuscript, 1996.

....intersection graph, is in this case associated with a path on a tree network. Two vertices are adjacent in the graph if the two corresponding paths are intersecting. This problem has recently received a growing attention due to its application to wavelength assignment in optical networks [RU94, BL97, GSR96] Several authors show an O( Delta) competitive deterministic algorithm for the problem of coloring online paths on a tree network (see for instance [BL97, GSR96] where Delta is the diameter of the graph. Bartal and Leonardi [BL97] also show an almost matching Omega Gamman = log ....

.... This problem has recently received a growing attention due to its application to wavelength assignment in optical networks [RU94, BL97, GSR96] Several authors show an O( Delta) competitive deterministic algorithm for the problem of coloring online paths on a tree network (see for instance [BL97, GSR96] where Delta is the diameter of the graph. Bartal and Leonardi [BL97] also show an almost matching Omega Gamman = log Delta) deterministic lower bound on a tree of diameter Delta = O(log n) where n is the number of vertices of the graph. In this paper we present the first ....

[Article contains additional citation context not shown here]

Y. Bartal and S. Leonardi. On-line routing in all-optical networks. In Proceedings of the 24th International Colloqium on Automata, Languages and Programming, LNCS 1256, pages 516--526. Springer-Verlag, 1997.

....new copy of the algorithm. This results in a multiplicative factor of 4 in the competitive ratio of the algorithm. The O(log n) competitive ratio is the best achievable up to a constant factor. A deterministic lower bound has been shown in [AAF 93] for a directed network. Bartal and Leonardi [BL97] show an Omega Gamma109 n) randomized lower bound for an undirected network. The algorithm can be extended to calls with limited duration. If D is the ratio between the maximum and the minimum duration, an O(log nD) competitive deterministic algorithm is presented in [AKP 93] In this ....

....For this problem, Slusarek [ S95] has shown that an on line algorithm can use a number of colors bounded by 3 Gamma 2, then yielding the same result for interval graph coloring. Path Coloring on Trees. An O(log n) competitive algorithm for trees has been proposed by several authors [BL97, BKS96, GSR96] The problem of on line path coloring on a tree can be reduced to the problem of coloring on line an O( inductive graph. A graph is d inductive if the vertices can be associated with numbers 1 through n in a way that every vertex is connected to at most d vertices with higher ....

[Article contains additional citation context not shown here]

Y. Bartal and S. Leonardi. On-line routing in all-optical networks. In Proceedings of the 24th International Colloqium on Automata, Languages and Programming, LNCS 1256, pages 516--526. Springer-Verlag, 1997.

....class of planar graphs, where n is the number of nodes in the network. Rabani [R96] improved the result for meshes to O(poly(log log n) The path coloring problem has also been studied in its on line version. Algorithms with an O(log n) competitive ratio have been devised by Bartal and Leonardi [BL96] for trees, trees of rings and meshes. The authors also present an Omega Gamma log n log log n ) lower bound for trees and an Omega Gamma 38 n) lower bound for meshes. For general networks, it has been shown that even randomized on line algorithms cannot approximate the optimal solution with ....

Y. Bartal and S. Leonardi. On-line routing in all-optical networks. Manuscript, 1996.

....communication request must be assigned with a specific wavelength, obeying the constraint that communication requests assigned with same wavelength are routed on edge disjoint paths. Competitive online algorithms for routing communications in optical networks have for instance been studied in [11, 12]. A large variety of other online network routing problems has been considered: calls can be preempted and or rerouted at some later time, the benefit obtained from a call can be proportional to the amount of assigned resources, collective communication, e.g. multicast communication, has been ....

Y. Bartal and S. Leonardi. On-line routing in all-optical networks. In Proc. of the 24th International Colloqium on Automata, Languages and Programming, Springer LNCS, Volume 1256, 516-526, 1997.

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Y. Bartal and S. Leonardi. On-line routing in all-optical networks. In Proceedings of the 24th International Colloquium on Automata, Languages and Programming ICALP '97, LNCS 1256, pages 516--526. Springer-Verlag, 1997.

No context found.

Y. Bartal and S. Leonardi. On-line routing in all-optical networks. In Proceedings of the 24th International Colloquium on Automata, Languages, and Programming, volume 1256 of Lecture Notes in Computer Science, pages 516--526. Springer-Verlag, 1997.

No context found.

Y. Bartal and S. Leonardi. On-line routing in all-optical networks. In Proc. of the 24th International Colloquium on Automata, Languages, and Programming, pages 516--526, 1997.

No context found.

Y. Bartal and S. Leonardi. On-line routing in all-optical networks. In Proc. of the 24th International Colloquium on Automata, Languages, and Programming, pages 516--526, 1997.

No context found.

Y. Bartal and S. Leonardi. On-line routing in all-optical networks. In Proc. of the 24th International Colloquium on Automata, Languages, and Programming, pages 516-526, 1997.

No context found.

Y. Bartal and S. Leonardi. On-line routing in all-optical networks. In Proc. of the 24th International Colloquium on Automata, Languages, and Programming, pages 516--526, 1997.

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Y. Bartal and S. Leonardi. On-line routing in all-optical networks. In In Proc. of the 24th International Colloquium on Automata, Languages, and Programming, pages 516-526, 1997.

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