Approximation algorithms for NP-complete problems on planar graphs
Journal of the ACM (JACM)
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
On the complexity of the regenerator placement problem in optical networks
Proceedings of the twenty-first annual symposium on Parallelism in algorithms and architectures
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)
Optimizing regenerator cost in traffic grooming
OPODIS'10 Proceedings of the 14th international conference on Principles of distributed systems
Optimizing regenerator cost in traffic grooming
Theoretical Computer Science
OPODIS'11 Proceedings of the 15th international conference on Principles of Distributed Systems
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
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The placement of regenerators in optical networks has become an active area of research during the last 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. While most of the research has focused on heuristics and simulations, the first theoretical study of the problem has been recently provided in [10], where the considered cost function is the number of locations in the network hosting regenerators. Nevertheless, in many situations a more accurate estimation of the real cost of the network is given by the total number of regenerators placed at the nodes, and this is the cost function we consider. 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 ln(d ċ p). We then study the case where G is a path, proving that the problem is NP-hard for any d, p ≥ 2, even if there are two edges of the path such that any lightpath uses at least one of them. Interestingly, we show that the problem is polynomial-time solvable in paths when all the lightpaths share the first edge of the path, as well as when the number of lightpaths sharing an edge is bounded. Finally, we generalize our model in two natural directions, which allows us to capture the model of [10] as a particular case, and we settle some questions that were left open in [10].