LCL problems on grids

Tutkimustuotos: Artikkeli kirjassa/konferenssijulkaisussavertaisarvioitu



  • Swiss Federal Institute of Technology Zurich
  • University of Helsinki
  • University Paris Diderot


LCLs or locally checkable labelling problems (e.g. maximal independent set, maximal matching, and vertex colouring) in the LOCAL model of computation are very well-understood in cycles (toroidal 1-dimensional grids): every problem has a complexity of O(1), Θ(log∗ n), or Θ(n), and the design of optimal algorithms can be fully automated. This work develops the complexity theory of LCL problems for toroidal 2-dimensional grids. The complexity classes are the same as in the 1-dimensional case: O(1), Θ(log∗ n), and Θ(n). However, given an LCL problem it is undecidable whether its complexity is Θ(log∗ n) or Θ(n) in 2-dimensional grids. Nevertheless, if we correctly guess that the complexity of a problem is Θ(log∗ n), we can completely automate the design of optimal algorithms. For any problem we can find an algorithm that is of a normal form A′·Sk, where A′ is a finite function, Sk is an algorithm for finding a maximal independent set in kth power of the grid, and k is a constant. Finally, partially with the help of automated design tools, we classify the complexity of several concrete LCL problems related to colourings and orientations.


OtsikkoPODC 2017 - Proceedings of the ACM Symposium on Principles of Distributed Computing
TilaJulkaistu - 26 heinäkuuta 2017
OKM-julkaisutyyppiA4 Artikkeli konferenssijulkaisuussa
TapahtumaACM Symposium on Principles of Distributed Computing - Washington, Yhdysvallat
Kesto: 25 heinäkuuta 201727 heinäkuuta 2017
Konferenssinumero: 36


ConferenceACM Symposium on Principles of Distributed Computing

ID: 15211850