On DRC‐covering of K<sub>n</sub> by cycles

Bermond, Jean‐Claude; Coudert, David; Yu, Mingjia

doi:10.1002/jcd.10040

Cited by 10 publications

(9 citation statements)

References 3 publications

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“…In both cases, the total number of vertices of the construction is N 2 2 , hence the lower bound is attained. Finally, one can check that in the constructions of [10], the length of the arcs involved in the covering of T N is in all cases bounded above by N 2 , and therefore all the cycles induce load 1. ■ Remark 4.1.…”

Section: Case C =mentioning

confidence: 99%

Traffic Grooming in Bidirectional WDM Ring Networks

Bermond

Coudert

Mufioz

et al. 2006

2006 International Conference on Transparent Optical Networks

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International audienceWe study the minimization of ADMs (Add-Drop Multiplexers) in Optical WDM Networks with Bidirectional Ring topology considering symmetric shortest path routing and all-to-all unitary requests. We insist on the statement of the problem, which had not been clearly stated before in the bidirectional case. Optimal solutions had not been found up to date. In particular, we study the case C = 2 and C = 3 (giving either optimal constructions or near-optimal solutions) and the case C = k(k+1)/2 (giving optimal decompositions for specific congruence classes of N). We state a general Lower Bound for all the values of C and N, and we improve this Lower Bound for C=2 and C=3 (when N=4t+3). We also include some comments about the simulation of the problem using Linear Programming

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Section: Case C =mentioning

confidence: 99%

Traffic Grooming in Bidirectional WDM Ring Networks

Bermond

Coudert

Mufioz

et al. 2006

2006 International Conference on Transparent Optical Networks

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“…Let Z be the ring of integers, and Zn be the residue ring of integers modulo n. Bermond et al [1] discussed the problem of DRC-covering when the logical graph I is a complete graph Kn (or a symmetric complete digraph K * n ) and the physical graph G is a cycle, and opened the problems of DRC-covering when the logical graph I is Kn m (or K n m ). Liang and Han [2] obtained an optimal DRC-covering if I is K , n n m (or K , n n m * ).…”

Section: Introductionmentioning

confidence: 99%

“…In the following, we quote the relation of reference [1]. Here we consider a covering problem arising from the decomposition of a survivable WDM network, where the communication requests are routed on subnetworks which are protected independently from each other.…”

Section: Introductionmentioning

confidence: 99%

On DRC-covering ofλ-fold complete graphs

Liang¹,

Han²

2014

Journal of Discrete Mathematical Sciences and Cryptography

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“…In [1], Bermond et al discussed the problem of DRC-covering for the logical graph I is the complete graph K n (or the symmetric complete digraph K * n ), and the physical graph G is a cycle. Bermond and Yu [2] extended the results to G be a torus (instead of cycle).…”

Section: Introductionmentioning

confidence: 99%

On DRC-cycle covering in optical networks

Liang

Xie

2014

Journal of High Speed Networks

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This paper consider the case when the physical graph G = C tn (a ring of size tn) and logical graph is λK t (n). We want to minimize the number of cycles ρ(n t , λ) in the DRC covering. For this problem, we obtain the optimal solutions when both n and t are odd. 42 Z. Liang and C. Xie / On DRC-cycle covering in optical networksgenerality; in first approximation, we can reduce it to minimize the number of cycles of the covering. We will restrict ourselves to a particular case of the general problem which is interesting for practical networks and shows already the difficulty of the problem. Mainly, we will suppose that the physical network is a ring and the set of requests is the All-to-All one.Compared to previous studies based on a similar approach (see [4,12]), we provide an analytical model and optimal solutions for the ring physical topology. A similar problem was considered in [3] and [5]. They use the same ring survivability conditions but their aim is to minimize the sum of the number of nodes of the rings.Routing problems are found both in the virtual graph and in the physical one. Here we consider a covering problem that the communication requests are routed on sub-networks which are protected independently from each other. We model the WDM network by a graph (called the physical graph), its nodes represent the optical switches and the edges the fiber-optics links. We will consider that the physical graph is either an undirected cycle of length tn, denoted by C tn , or the symmetric directed cycle C * tn . Routing a request over physical graph G consists in finding a path over G between the pair of nodes communicating in the request. We can model all the requests as the edge set of a logical graph I undirected or not. The nodes represent the nodes of the physical graph and the edges correspond to the requests between these nodes. One constraint that each cycle formed by some requests must be routed node disjoint over the physical graph G. We call this property the disjoint routing constraint (DRC).Problem 1.1. Find a cycle decomposition or a cycle covering satisfying DRC property of the edges of I with an associated routing over G such that the number of cycles is minimized. Z. Liang and C. Xie / On DRC-cycle covering in optical networksthe number of cycles t 2 − t

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On DRC‐covering of K_n by cycles

Cited by 10 publications

References 3 publications

Traffic Grooming in Bidirectional WDM Ring Networks

Traffic Grooming in Bidirectional WDM Ring Networks

On DRC-covering ofλ-fold complete graphs

On DRC-cycle covering in optical networks

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On DRC‐covering of Kn by cycles

Cited by 10 publications

References 3 publications

Traffic Grooming in Bidirectional WDM Ring Networks

Traffic Grooming in Bidirectional WDM Ring Networks

On DRC-covering ofλ-fold complete graphs

On DRC-cycle covering in optical networks

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On DRC‐covering of K_n by cycles