Wavelength Assignment in WDM Rings with Splitable Lightpaths zy Gruia Ciilinescu zyxwv * Peng-Jun Wan Dept. of Computer Science, Illinois Institute of Technology, Chicago, IL 6061 6 E-mail: { calinesc,wan}@cs.iit.edu Abstract zyxwvuts This paper presents a new practical approximation algo- rithmfor wavelength assignment to splitable lightpaths over WDM rings, with the objective zyxwvuts of minimizing the number of SONET ADMs. Allowing the splitting of traffic streams can significantly reduce the number of required zyxwvutsrq ADMs. Moreover, while finding the best assignment is proved to be NP-Hard, the problem seems easier to approximate than the variation when traffic streams cannot be split. In the worst case, the output of the new polynomial-time algorithm is at most 25% more than the optimum solution. This result is significantly better than the best known approximation ra- tio for non-splitable traffic streams. Keywords: wavelength division multiplexing (WDM), optical networks, SONET, add-drop multiplexer (ADM), WADM, grooming, approximation algorithm. 1 Introduction WDM self-healing ring (SHR) networks are being de- ployed by a growing number of telecom carriers to sup- port multiple high-level SONET/SDH rings [7] over a sin- gle physical fiber optical ring. One of the most fundamen- tal network design problems for WDM networks is the as- signment of wavelengths to a given set of traffic streams. While most of the previous works attempt to minimize the number of wavelengths required or the amount of blocking for the given set of traffic streams [l, zyxwvu 5,9, 10, 31, it was ar- gued in [4,6] that unless the wavelength limit is exceeded, the first-order optimization goal should be to minimize the overall network cost which is dominated by the number of required SONET add/drop multiplexers (ADMs) instead of the number of wavelengths. In a WDM SHR, each (logical) SONET ring requires a SONET ADM at each node inside it and no ADM at any other node outside it due to the opti- cal bypass capability of optical add-drop multiplexers. Thus *Work zyxwvutsrqp performed in part at Georgia Institute of Technology and sup- ported in part by NSF grant CCR-9732746 the SONET ADM cost of a SONET ring is equal to the size of this SONET ring, i.e., the number of nodes it contains. The total SONET ADM cost is then the sum of the costs of all SONET rings. Alternatively, the SONET ADM cost of a node is equal to the number of SONET rings that contain this node, and the total ADM cost is the sum of the costs of all nodes. It was shown in [6] that minimizing the number of SONET ADMs is intrinsically different from the minimiz- ing the number of wavelengths, and there exist cases where the two minima cannot be simultaneously achieved. Recently, many works [4, 81 studied the wavelength as- signment to lightpaths over WDM rings to minimize the SONET ADMs. In each fiber ring, a traffic stream can be represented as a (directed) circular arc over the fiber ring, and an instance of ADM-minimization problem is a set A of circular arcs. Depending on the implementation, the circu- lar arcs are or are not be allowed to be split [6]. If splitting is not allowed, a valid wavelength assignment corresponds to a partition of A into groups of non-overlapping circular arcs (a set of circular arcs are said to be non-overlapping if the in- teriors of any pair of arcs have empty intersection). If split- ting is allowed, then a valid wavelength assignment consists of a choice of splitting each arc of A, thus obtaining A', and then a partition of A' into groups of non-overlappingcircular arcs. In either case, each group of non-overlapping circular arcs can be carried in a wavelength and thus form a logical SONET ring. Finding an optimal solution without splits was shown to be "-Hard in [8] and a number of polynomial- time approximations algorithms were proposed in both [4] and [SI. The best known worst-case approximationratio for non-splitable arcs is 1.5 ([2]), or in other words the output of the algorithm presented by [2] is proved to have cost at most 50% more than the optimum solution. Following the same argument as in [8], this paper shows that finding an optimal solution with splits is also "-Hard. In [4] it was first argued that splitting lightpaths has the po- tential to significantly reduce the number of ADMs. Split- ting is achieved by placing two ADMs and electrically trans- ferring the data between two wavelengths. A simple exam- ple presented in this paper shows that splitting can reduce 216 1087-4089/00 $10.00 zyxwvutsrqpo 0 2000 IEEE Authorized licensed use limited to: CityU. Downloaded on May 22,2010 at 09:18:21 UTC from IEEE Xplore. Restrictions apply.