Minimizing request blocking in all-optical rings

Abstract

Abstract-In all-optical 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.Here we study the problem for rings under both the undirected and the directed settings, corresponding to symmetric and oneway communication respectively. The problem in graph-theoretic terms can be formulated as the MAXIMUM ROUTING AND PATH COLORING PROBLEM. We present a Chain-and-Matching technique for routing requests and coloring the corresponding paths which gives constant approximations for both the undirected and the directed cases. For the undirected problem we obtain a

Approximation Algorithms for Edge-Disjoint Paths and Unsplittable Flow

“…This approach can be extended to give a polynomial-time algorithm for bidirected spiders as well, as shown for a more general problem by Erlebach and Vukadinović [22]. In undirected or bidirected rings, MEDP can also be solved optimally in polynomial time [58,49].…”

“…By a general reduction [17,2], a ρ-approximation algorithm for MEDP can be converted into an approximation algorithm with ratio at most 1/(1 − e −1/ρ ) ≤ ρ + 1 for MAXPC. In some cases, better approximation ratios for MAXPC have been obtained using more direct approaches, for example by Nomikos et al for MAXPC in undirected and bidirected rings [49].…”

Wavelength Management in WDM Rings to Maximize the Number of Connections

“…We consider not only the basic iterative algorithm that iteratively computes link-disjoint paths but also more involved algorithms. We show that even the basic iterative algorithm combined with algorithm CL has approximation ratio 18/13 ≈ 1.38462 and 60/41 ≈ 1.46341 in undirected and bidirected rings, respectively, significantly improving the e e−1 bound of [1,24] and the ratios of the algorithms in [17,18]. More involved iterative algorithms that use local search algorithms for computing set packings are proved to achieve approximation ratios 4/3 and 719/509 + ≈ 1.41257, respectively.…”

“…Hence, we obtain that the benefit of algorithm I&3LS when it terminates by assigning the last wavelength to a single connection is at least Next we present algorithms that improve the 11/7 approximation bound of [18] in bidirected rings. We denote by bCL-I the algorithm obtained by combining algorithm CL with the basic iterative algorithm that iteratively computes compatible sets of connections on bidirected rings.…”

“…Awerbuch et al [1] (see also [24]) show that algorithms that iteratively call link-disjoint paths algorithms to compute solutions to maxRPC with arbitrary w have slightly worse approximation ratio than the ratio of the algorithm that is used to compute link-disjoint paths. In undirected and bidirected rings, link-disjoint paths of maximum size can be computed in polynomial-time yielding iterative algorithms with approximation ratio e e−1 ≈ 1.58198 [24] (see also the discussion in [18]). The best known approximation algorithms for maxRPC (and maxPC) in undirected rings has approximation ratio 3/2 [17,18] while an 11/7-approximation algorithm for maxRPC in bidirected rings is presented in [18].…”