A 10/7 + $ \epsilon$ Approximation for Minimizing the Number of ADMs in SONET Rings

Shalom, Mordechai; Zaks, Shmuel

doi:10.1109/tnet.2007.906638

Cited by 15 publications

(17 citation statements)

References 18 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…In [6,17,9] algorithms with improved approximation guarantees are presented, where the approximation ratios are 3/2, 10/7 + ϵ and 47/34 + ϵ, respectively. For general topology, approximation algorithms with approximation ratio of 8 5 and 1.5 + ϵ are presented in [5,8].…”

Section: Minimization Of Switching Costmentioning

confidence: 99%

On-line maximum matching in complete multi-partite graphs with an application to optical networks

Shalom

Wong

Zaks

2016

Discrete Applied Mathematics

Self Cite

View full text Add to dashboard Cite

a b s t r a c tFinding a maximum matching in a graph is a classical problem. The on-line versions of the problem in which the vertices and/or edges of the graph are given one at a time and an algorithm has to calculate a matching incrementally have been studied for more than two decades. Many variants of the problem are considered in the literature. The pioneering work (Karp, 1990) considers a bipartite graph where the vertices of one part are revealed one at a time together with their incident edges. In this work we consider maximal d-colorable graphs which are exactly the complete d-partite graphs. The vertices arrive one at a time together with their incident edges, or equivalently with their corresponding colors in some given d-coloring of the graph. We present an optimal 2/3-competitive deterministic algorithm for this on-line problem.This problem is closely related to that of minimizing the cost of line terminals in star topology optical network. We consider lightpaths arriving in an on-line fashion on a given star network. Our result implies a tight 10/9-competitive algorithm for finding a wavelength assignment minimizing the cost of line terminals in such a network.

show abstract

Section: Minimization Of Switching Costmentioning

confidence: 99%

On-line maximum matching in complete multi-partite graphs with an application to optical networks

Shalom

Wong

Zaks

2016

Discrete Applied Mathematics

Self Cite

View full text Add to dashboard Cite

show abstract

“…The problem was introduced in [8] for the ring topology. An approximation algorithm for the ring topology with approximation ratio of 3 2 was presented in [4], and was improved in [11,5] to 10 7 + and 10 7 , respectively. For general topology [6] described an algorithm with approximation ratio of 8 5 .…”

Section: Previous Workmentioning

confidence: 99%

Optimal on-line colorings for minimizing the number of ADMs in optical networks

Shalom

Wong

Zaks

2010

Journal of Discrete Algorithms

Self Cite

View full text Add to dashboard Cite

We consider the problem of minimizing the number of ADMs in optical networks. All previous theoretical studies of this problem dealt with the off-line case, where all the lightpaths are given in advance. In a real-life situation, the requests (lightpaths) arrive at the network on-line, and we have to assign them wavelengths so as to minimize the switching cost. This study is thus of great importance in the theory of optical networks. We present a deterministic on-line algorithm for the problem, and show its competitive ratio to be 7 4 . We show that this result is best possible in general. Moreover, we show that even for the ring topology network there is no on-line algorithm with competitive ratio better than 7 4 . We show that on path topology the competitive ratio of the algorithm is 3 2 . This is optimal for in this topology. The lower bound on ring topology does not hold when the ring is of bounded size. We analyze the triangle topology and show a tight bound of 5 3 for it. The analyses of the upper bounds, as well as those for the lower bounds, are all using a variety of proof techniques, which are of interest by their own, and which might prove helpful in future research on the topic.

show abstract

“…These non-divisible problems were studied before in [5], [6], [8], [2]- [4], and [7]. Cǎlinescu and Wan [2] provided a 3 2 -approximation algorithms for both non-divisible problems.…”

Section: Introduction Wdm (Wavelength Division Multiplexing)/sonet (mentioning

confidence: 99%

“…In [3] we considered the non-divisible arc version problem and obtained a 10 7 -approximation algorithm. A different approximation algorithm of approximation ratio 10 7 + ε was given by Shalom and Zaks [7]. In [4] we considered the non-divisible chord version problem and obtained a 10 7 -approximation algorithm as well (using a different approach).…”

Section: Introduction Wdm (Wavelength Division Multiplexing)/sonet (mentioning

confidence: 99%

SONET ADMs Minimization with Divisible Paths

Epstein

Levin

2007

Algorithmica

View full text Add to dashboard Cite

We consider an optical routing problem. SONET add-drop multiplexers (ADMs) are the dominant cost factor in SONET/WDM rings. The number of SONET ADMs required by a set of traffic streams is determined by the routing and wavelength assignment of the traffic streams. In this paper we consider the version where a traffic stream may be divided into several parts and assigned different wavelengths. A specific division may increase or decrease the number of ADMs needed for a given input. Following previous work, we consider two versions. In the arc version the route of each traffic stream is given as input, and we need to decide on divisions of streams, and then to assign wavelengths so as to minimize the total number of used SONET ADMs. In the chord version the route is not prespecified, but is assigned by the algorithm, and only after this step are the divisions done and wavelengths assigned. The previously best known approximation algorithm for the arc version has a performance guarantee of 5 4 = 1.25 whereas the previously best known approximation algorithm for the chord version has a performance guarantee of 3 2 = 1.5. We improve both these results. We present a 36 29 ≈ 1.24138-approximation algorithm for the arc version and a 7 5 = 1.4-approximation algorithm for the chord version.

show abstract

A 10/7 + $ \epsilon$ Approximation for Minimizing the Number of ADMs in SONET Rings

Cited by 15 publications

References 18 publications

On-line maximum matching in complete multi-partite graphs with an application to optical networks

On-line maximum matching in complete multi-partite graphs with an application to optical networks

Optimal on-line colorings for minimizing the number of ADMs in optical networks

SONET ADMs Minimization with Divisible Paths

Contact Info

Product

Resources

About