Maximum bounded 3-dimensional matching is MAX SNP-complete
Information Processing Letters
On optimal traffic grooming in WDM rings
Proceedings of the 2001 ACM SIGMETRICS international conference on Measurement and modeling of computer systems
Ruling Out PTAS for Graph Min-Bisection, Densest Subgraph and Bipartite Clique
FOCS '04 Proceedings of the 45th Annual IEEE Symposium on Foundations of Computer Science
Networks
Algorithmic Graph Minor Theory: Decomposition, Approximation, and Coloring
FOCS '05 Proceedings of the 46th Annual IEEE Symposium on Foundations of Computer Science
Approximating the traffic grooming problem
ISAAC'05 Proceedings of the 16th international conference on Algorithms and Computation
Better bounds for minimizing SONET ADMs
WAOA'04 Proceedings of the Second international conference on Approximation and Online Algorithms
Traffic grooming in WDM networks
IEEE Communications Magazine
Traffic grooming in path, star, and tree networks: complexity, bounds, and algorithms
IEEE Journal on Selected Areas in Communications - Part Supplement
Traffic grooming in WDM networks: past and future
IEEE Network: The Magazine of Global Internetworking
Approximating the Traffic Grooming Problem with Respect to ADMs and OADMs
Euro-Par '08 Proceedings of the 14th international Euro-Par conference on Parallel Processing
Traffic Grooming in Unidirectional WDM Rings with Bounded Degree Request Graph
Graph-Theoretic Concepts in Computer Science
Degree-Constrained Subgraph Problems: Hardness and Approximation Results
Approximation and Online Algorithms
Parameterized complexity of the smallest degree-constrained subgraph problem
IWPEC'08 Proceedings of the 3rd international conference on Parameterized and exact computation
Decomposition, approximation, and coloring of odd-minor-free graphs
SODA '10 Proceedings of the twenty-first annual ACM-SIAM symposium on Discrete Algorithms
Survivable impairment-aware traffic grooming in WDM rings
Proceedings of the 23rd International Teletraffic Congress
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Traffic grooming is a central problem in optical networks. It refers to pack low rate signals into higher speed streams, in order to improve bandwidth utilization and reduce network cost. In WDM networks, the most accepted criterion is to minimize the number of electronic terminations, namely the number of SONET Add-Drop Multiplexers (ADMs). In this article we focus on ring and path topologies. On the one hand, we provide the first inapproximability result for TRAFFIC GROOMING for fixed values of the grooming factor g, answering affirmatively the conjecture of Chow and Lin (Networks, 44:194-202, 2004). More precisely, we prove that RING TRAFFIC GROOMING for fixed g ≥ 1 and PATH TRAFFIC GROOMING for fixed g ≥ 2 are APX-complete. That is, they do not accept a PTAS unless P = NP. Both results rely on the fact that finding the maximum number of edge-disjoint triangles in a graph (and more generally cycles of length 2g +1 in a graph of girth 2g +1) is APX-complete. On the other hand, we provide a polynomial-time approximation algorithm for RING and PATH TRAFFIC GROOMING, based on a greedy cover algorithm, with an approximation ratio independent of g. Namely, the approximation guarantee is O(n1/3 log2 n) for any g ≥ 1, n being the size of the network. This is useful in practical applications, since in backbone networks the grooming factor is usually greater than the network size. As far as we know, this is the first approximation algorithm with this property. Finally, we improve this approximation ratio under some extra assumptions about the request graph.