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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)

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.

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Copyright information

© Springer International Publishing Switzerland 2014

Authors and Affiliations

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

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