Abstract
We study the complexity of the Channel Assignment problem. By applying the meet-in-the-middle approach we get an algorithm for the ℓ-bounded Channel Assignment (when the edge weights are bounded by ℓ) running in time \(O^*((2\sqrt{\ell+1})^n)\). This is the first algorithm which breaks the (O(ℓ))n barrier. We extend this algorithm to the counting variant, at the cost of slightly higher polynomial factor.
A major open problem asks whether Channel Assignment admits a O(c n)-time algorithm, for a constant c independent of ℓ. We consider a similar question for Generalized T -Coloring, a CSP problem that generalizes Channel Assignment. We show that Generalized T -Coloring does not admit a \(2^{2^{o\left(\sqrt{n}\right)}} {\rm poly}(r)\)-time algorithm, where r is the size of the instance.
Research supported by National Science Centre of Poland, grant number UMO-2013/09/B/ST6/03136.
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Kowalik, Ł., Socała, A. (2014). Assigning Channels via the Meet-in-the-Middle Approach. In: Ravi, R., Gørtz, I.L. (eds) Algorithm Theory – SWAT 2014. SWAT 2014. Lecture Notes in Computer Science, vol 8503. Springer, Cham. https://doi.org/10.1007/978-3-319-08404-6_25
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DOI: https://doi.org/10.1007/978-3-319-08404-6_25
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