Approximation algorithms for NP-complete problems on planar graphs
Journal of the ACM (JACM)
Approximation of k-set cover by semi-local optimization
STOC '97 Proceedings of the twenty-ninth annual ACM symposium on Theory of computing
Journal of Combinatorial Theory Series B
Some APX-completeness results for cubic graphs
Theoretical Computer Science
Approximation algorithms
Computers and Intractability: A Guide to the Theory of NP-Completeness
Computers and Intractability: A Guide to the Theory of NP-Completeness
Information theoretic approach to traffic adaptive WDM networks
IEEE/ACM Transactions on Networking (TON)
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
MPLS Label Stacking on the Line Network
NETWORKING '09 Proceedings of the 8th International IFIP-TC 6 Networking Conference
Hardness and approximation of traffic grooming
Theoretical Computer Science
Inapproximability of Vertex Cover and Independent Set in Bounded Degree Graphs
CCC '09 Proceedings of the 2009 24th Annual IEEE Conference on Computational Complexity
The regenerator location problem
Networks - Network Optimization (INOC 2007)
Brief announcement: on regenerator placement problems in optical networks
Proceedings of the twenty-second annual ACM symposium on Parallelism in algorithms and architectures
On the complexity of the regenerator placement problem in optical networks
IEEE/ACM Transactions on Networking (TON)
Traffic grooming in path, star, and tree networks: complexity, bounds, and algorithms
IEEE Journal on Selected Areas in Communications - Part Supplement
Parameterized Complexity
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The placement of regenerators in optical networks has become an active area of research during the last few years. Given a set of lightpaths in a network G and a positive integer d, regenerators must be placed in such a way that in any lightpath there are no more than d hops without meeting a regenerator. The cost function we consider is given by the total number of regenerators placed at the nodes, which we believe to be a more accurate estimation of the real cost of the network than the number of locations considered in the work of Flammini et al. (IEEE/ACM Trans. Netw., vol. 19, no. 2, pp. 498-511, Apr. 2011). Furthermore, in our model we assume that we are given a finite set of p possible traffic patterns (each given by a set of lightpaths), and our objective is to place the minimum number of regenerators at the nodes so that each of the traffic patterns is satisfied. While this problem can be easily solved when d = 1 or p = 1, we prove that for any fixed d, p ≥ 2, it does not admit a PTAS, even if G has maximum degree at most 3 and the lightpaths have length O(d). We complement this hardness result with a constant-factor approximation algorithm with ratio (dċp). We then study the case where G is a path, proving that the problem is polynomial-time solvable for two particular families of instances. Finally, we generalize our model in two natural directions, which allows us to capture the model of Flammini et al. as a particular case, and we settle some questions that were left open therein.