Assigning Channels via the Meet-in-the-Middle Approach

  • Łukasz Kowalik
  • Arkadiusz Socała
Part of the Lecture Notes in Computer Science book series (LNCS, volume 8503)


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.


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  1. 1.
    Björklund, A., Husfeldt, T., Koivisto, M.: Set partitioning via inclusion-exclusion. SIAM J. Comput. 39(2), 546–563 (2009)CrossRefzbMATHMathSciNetGoogle Scholar
  2. 2.
    Cygan, M., Kowalik, L.: Channel assignment via fast zeta transform. Inf. Process. Lett. 111(15), 727–730 (2011)CrossRefzbMATHMathSciNetGoogle Scholar
  3. 3.
    Fomin, F.V., Kratsch, D., Woeginger, G.J.: Exact (exponential) algorithms for the dominating set problem. In: Hromkovič, J., Nagl, M., Westfechtel, B. (eds.) WG 2004. LNCS, vol. 3353, pp. 245–256. Springer, Heidelberg (2004)CrossRefGoogle Scholar
  4. 4.
    Hale, W.: Frequency assignment: Theory and applications. Proceedings of the IEEE 68(12), 1497–1514 (1980)CrossRefGoogle Scholar
  5. 5.
    Horowitz, E., Sahni, S.: Computing partitions with applications to the knapsack problem. J. ACM 21(2), 277–292 (1974)CrossRefzbMATHMathSciNetGoogle Scholar
  6. 6.
    Husfeldt, T., Paturi, R., Sorkin, G.B., Williams, R.: Exponential Algorithms: Algorithms and Complexity Beyond Polynomial Time (Dagstuhl Seminar 13331). Dagstuhl Reports 3(8), 40–72 (2013)Google Scholar
  7. 7.
    Impagliazzo, R., Paturi, R.: On the complexity of k-sat. J. Comput. Syst. Sci. 62(2), 367–375 (2001)CrossRefzbMATHMathSciNetGoogle Scholar
  8. 8.
    Junosza-Szaniawski, K., Rzążewski, P.: An exact algorithm for the generalized list T-coloring problem. CoRR, abs/1311.0603 (2013)Google Scholar
  9. 9.
    Král, D.: An exact algorithm for the channel assignment problem. Discrete Applied Mathematics 145(2), 326–331 (2005)CrossRefzbMATHMathSciNetGoogle Scholar
  10. 10.
    McDiarmid, C.J.H.: On the span in channel assignment problems: bounds, computing and counting. Discrete Mathematics 266(1-3), 387–397 (2003)CrossRefzbMATHMathSciNetGoogle Scholar
  11. 11.
    Traxler, P.: The time complexity of constraint satisfaction. In: Grohe, M., Niedermeier, R. (eds.) IWPEC 2008. LNCS, vol. 5018, pp. 190–201. Springer, Heidelberg (2008)CrossRefGoogle Scholar

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© Springer International Publishing Switzerland 2014

Authors and Affiliations

  • Łukasz Kowalik
    • 1
  • Arkadiusz Socała
    • 1
  1. 1.University of WarsawPoland

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