Untitled

Călinescu, Gruia; Wan, Peng‐Jun

doi:10.1023/a:1019525904862

Cited by 37 publications

(1 citation statement)

References 10 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…The ADM minimization problem is defined in [6] for ring topology and g = 1. It is proven to be NP-complete in [7], and an 3/2-approximation algorithm was presented in the study [8]. This result is improved in [9,10] to 10/7 + and 10/7, respectively.…”

Section: Related Workmentioning

confidence: 94%

The Traffic Grooming Problem in Optical Networks with Respect to ADMs and OADMs: Complexity and Approximation

et al. 2021

View full text Add to dashboard Cite

All-optical networks transmit messages along lightpaths in which the signal is transmitted using the same wavelength in all the relevant links. We consider the problem of switching cost minimization in these networks. Specifically, the input to the problem under consideration is an optical network modeled by a graph G, a set of lightpaths modeled by paths on G, and an integer g termed the grooming factor. One has to assign a wavelength (modeled by a color) to every lightpath, so that every edge of the graph is used by at most g paths of the same color. A lightpath operating at some wavelength λ uses one Add/Drop multiplexer (ADM) at both endpoints and one Optical Add/Drop multiplexer (OADM) at every intermediate node, all operating at a wavelength of λ. Two lightpaths, both operating at the same wavelength λ, share the ADMs and OADMs in their common nodes. Therefore, the total switching cost due to the usage of ADMs and OADMs depends on the wavelength assignment. We consider networks of ring and path topology and a cost function that is a convex combination α·|OADMs|+(1−α)|ADMs| of the number of ADMs and the number of OADMs deployed in the network. We showed that the problem of minimizing this cost function is NP-complete for every convex combination, even in a path topology network with g=2. On the positive side, we present a polynomial-time approximation algorithm for the problem.

show abstract

Section: Related Workmentioning

confidence: 94%

The Traffic Grooming Problem in Optical Networks with Respect to ADMs and OADMs: Complexity and Approximation

et al. 2021

View full text Add to dashboard Cite

show abstract

Approximating the Traffic Grooming Problem

Flammini

Moscardelli

Shalom

et al. 2005

Algorithms and Computation

View full text Add to dashboard Cite

The problem of grooming is central in studies of optical networks. In graph-theoretic terms, this can be viewed as assigning colors to the lightpaths so that at most g of them (g being the grooming factor) can share one edge. The cost of a coloring is the number of optical switches (ADMs); each lightpath uses two ADMs, one at each endpoint, and in case g lightpaths of the same wavelength enter through the same edge to one node, they can all use the same ADM (thus saving g − 1 ADMs). The goal is to minimize the total number of ADMs. This problem was shown to be NP-complete for g = 1 and for a general g. Exact solutions are known for some specific cases, and approximation algorithms for certain topologies exist for g = 1. We present an approximation algorithm for this problem. For every value of g the running time of the algorithm is polynomial in the input size, and its approximation ratio for a wide variety of network topologies-including the ring topology-is shown to be 2 ln g + o(ln g). This is the first approximation algorithm for the grooming problem with a general grooming factor g.

show abstract

SONET ADMs Minimization with Divisible Paths

Epstein

Levin

2006

Approximation and Online Algorithms

View full text Add to dashboard Cite

Untitled

Cited by 37 publications

References 10 publications

The Traffic Grooming Problem in Optical Networks with Respect to ADMs and OADMs: Complexity and Approximation

The Traffic Grooming Problem in Optical Networks with Respect to ADMs and OADMs: Complexity and Approximation

Approximating the Traffic Grooming Problem

SONET ADMs Minimization with Divisible Paths

Contact Info

Product

Resources

About