Space-Efficient Counting in Graphs on Surfaces

@article{Braverman2009SpaceEfficientCI,
  title={Space-Efficient Counting in Graphs on Surfaces},
  author={Mark Braverman and Raghav Kulkarni and Sambuddha Roy},
  journal={computational complexity},
  year={2009},
  volume={18},
  pages={601-649}
}
Abstract.We consider the problem of counting the number of spanning trees in planar graphs. We prove tight bounds on the complexity of the problem, both in general and especially in the modular setting. We exhibit the problem to be complete for Logspace when the modulus is 2k, for constant k. On the other hand, we show that for any other modulus and in the non-modular case, our problem is as hard in the planar case as for the case of arbitrary graphs. The techniques used are algebraic… CONTINUE READING

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