Approximation Algorithms for Many-to-Many Traffic Grooming in WDM Mesh Networks Mohammad A. Saleh Ahmed E. Kamal Department of Electrical and Computer Engineering, Iowa State University, Ames, IA 50011 Email: {msaleh,kamal}@iastate.edu Abstract—A large number of network applications today allow several users to interact together using the many-to-many service mode. In many-to-many communication, also referred to as group communication, a session consists of a group of users (we refer to them as members), where each member transmits its traffic to all other members in the same group. In this paper, we address the problem of grooming sub-wavelength many-to-many traffic (e.g., OC-3) into high-bandwidth wavelength channels (e.g., OC-192) in WDM mesh networks. I. I NTRODUCTION In wavelength routing networks, using wavelength division multiplexing (WDM), it is feasible to have hundreds of wave- lengths per fiber each operating at 10 to 40 Gbps. Bandwidth requirements of user sessions, however, are usually of sub- wavelength granularities. For example, an MPEG compressed HDTV channel requires less than 20 Mbps of bandwidth. In order to reduce this huge bandwidth gap, traffic grooming was introduced to allow a number of sessions with sub-wavelength granularities to share the bandwidth of a wavelength channel. Early network applications such as TELNET and FTP are characterized as unicast or ”one-to-one”. A large portion of network applications today, however, are of the multipoint type. For example, video distribution and file distribution are examples of multicast or ”one-to-many” applications, while resource discovery and data collection are examples of many- to-one or ”inverse multicasting” applications. Recently, an- other set of multipoint network applications has emerged such as multimedia conferencing, e-science applications, distance learning, distributed simulations, and collaborative processing [23]. In these applications, each of the participating entities This research was supported in part by grant CNS-0626741 from the National Science Foundation. Fig. 1. A many-to-many session with members {A, B, C, D} each with traffic denoted as a, b, c and d, respectively. both contributes and receives information to and from the other entities in the same communication session, and therefore are characterized as ”many-to-many”. In many-to-many communi- cation, also referred to as group communication [22], a session consists of a group of users (we refer to them as members), where each member transmits its traffic to all other members in the same group (see Fig. 1). Most of the early work on traffic grooming has focused on unicast traffic on ring and mesh topologies. Since a large por- tion of network applications today are of the multipoint type, many of the recent studies on traffic grooming has focused on multicast and many-to-one traffic types. In this work, we consider the many-to-many traffic grooming problem in WDM mesh networks, which is an important new research problem. In this problem, a collection of many-to-many session requests, each with an arbitrary sub-wavelength traffic demand, are given and the objective is to find a set of lightpaths and to find the corresponding routing and grooming of each of the traffic demands onto these lightpaths. For a complete design of the WDM network, the traffic grooming problem is followed by the routing and wavelength assignment (RWA) problem which finds routes and assign wavelengths to each of the lightpaths on the WDM network. The objective of the RWA problem is to minimize the total number of wavelengths used. The RWA has been extensively studied in the literature and it has been shown to be NP-complete. Therefore, in this work, we focus on the many-to-many traffic grooming problem. However, for completeness and for comparison purposes, we use one of the best existing heuristics for the RWA problem (the LFAP heuristic [18]). The cost of a WDM network is dominated by the cost of higher layer electronic ports such as IP router ports, MPLS b,c,d a b a , b, c d c The cost of a WDM network is dominated by the cost of higher layer electronic ports (i.e., transceivers). A transceiver is needed for each initiation and termination of a lightpath. Therefore, our objective is to minimize the total number of lightpaths established. Unfortunately, the grooming problem even with unicast traffic has been shown to be NP-hard. For a number of special cases where the many-to-many traffic grooming problem is tractable, we efficiently derive the optimal solution, while in the general case, we introduce two novel approximation algorithms. We also consider the routing and wavelength assignment problem with the objective of minimizing the number of wavelengths used. Through extensive experiments, we show that the two algorithms use a number of lightpaths that is very close to that of a derived lower bound. Also, we compare the two algorithms on the several costs mentioned in the paper including the number of lightpaths and the number of wavelengths used.