SIAM Journal on Discrete Mathematics
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
Some optimal inapproximability results
Journal of the ACM (JACM)
Genome Rearrangements and Sorting by Reversals
SIAM Journal on Computing
Packing triangles in bounded degree graphs
Information Processing Letters
Networks
Algorithmic Graph Minor Theory: Decomposition, Approximation, and Coloring
FOCS '05 Proceedings of the 46th Annual IEEE Symposium on Foundations of Computer Science
Theoretical Computer Science
Ruling Out PTAS for Graph Min-Bisection, Dense k-Subgraph, and Bipartite Clique
SIAM Journal on Computing
Approximating the traffic grooming problem
Journal of Discrete Algorithms
On the complexity of the traffic grooming problem in optical networks
FUN'07 Proceedings of the 4th international conference on Fun with algorithms
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
Placing regenerators in optical networks to satisfy multiple sets of requests
ICALP'10 Proceedings of the 37th international colloquium conference on Automata, languages and programming: Part II
A new multi-granularity grooming algorithm based on traffic partition in IP over WDM networks
Computer Networks: The International Journal of Computer and Telecommunications Networking
On approximating the d-girth of a graph
SOFSEM'11 Proceedings of the 37th international conference on Current trends in theory and practice of computer science
Approximation algorithms for grooming in optical network design
Theoretical Computer Science
Parameterized complexity of finding small degree-constrained subgraphs
Journal of Discrete Algorithms
Traffic grooming in star networks via matching techniques
SIROCCO'10 Proceedings of the 17th international conference on Structural Information and Communication Complexity
On the complexity of the regenerator cost problem in general networks with traffic grooming
OPODIS'11 Proceedings of the 15th international conference on Principles of Distributed Systems
On the approximability of some degree-constrained subgraph problems
Discrete Applied Mathematics
Edge-Partitioning Regular Graphs for Ring Traffic Grooming with a Priori Placement of the ADMs
SIAM Journal on Discrete Mathematics
Placing regenerators in optical networks to satisfy multiple sets of requests
IEEE/ACM Transactions on Networking (TON)
On approximating the d-girth of a graph
Discrete Applied Mathematics
Hi-index | 5.23 |
Traffic grooming is a central problem in optical networks. It refers to packing 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 an inapproximability result for Traffic Grooming for fixed values of the grooming factor g, answering affirmatively the conjecture of Chow and Lin [T. Chow, P. Lin, The ring grooming problem, Networks 44 (2004), 194-202]. 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 tripartite graph (and more generally cycles of length 2g+1 in a (2g+1)-partite 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(n^1^/^3log^2n) 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. Finally, we improve this approximation ratio under some extra assumptions about the request graph.