The chord version for SONET ADMs minimization

Abstract

We consider a problem which arises in optical routing. WDM/SONET rings are a network architecture used by telecommunications carriers for traffic streams. The dominant cost factor in such networks is the total number of add-drop multiplexers (ADMs) used. A list of traffic streams to be routed between pairs of nodes is given. In this paper we consider the problem where we need to assign a route and a wavelength to each traffic stream, minimizing the total number of used SONET ADMs. This is called the chord version of the SONET ADMs minimization problem, to denote the fact that the routing is not given a priori. The best previously known approximation algorithms for this problem have the performance guarantee of 3 2 . We present an improved algorithm with performance guarantee of exactly 10 7 ≈ 1.42857. Moreover, we study some natural heuristics for this problem, and give tight analysis of their approximation ratios.

SONET ADMs Minimization with Divisible Paths

“…The lengths of such chains are exactly 2k > n/2, and therefore IM does not continue. The cost is therefore PIM = 3(k − 1) + 9(k − 1), and we get the ratio 4 3 . The performance of GP-ER on this instance is better than PIM.…”

“…That is, the same wavelength is used on all the links of the path established for a traffic stream. Such earlier studies include [6], [5], [8], and [2]- [4]. We later describe some of their results.…”

“…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.…”

“…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).…”

“…For the chord version, we combine D-DAG and P-ER into Chord-Combination (CC). The algorithm D-DAG was already introduced in [2] where it is called the Edge Avoidance Routing algorithm, and further discussed and used in [4]. This algorithm orients the edges so that the resulting graph is acyclic, and then solves this instance optimally.…”