Resolution complexity of random constraint satisfaction problems: Another half of the story

  • Authors:

  • Yong Gao;Joseph Culberson

  • Affiliations:

  • Department of Computing Science, University of Alberta, Edmonton, Alta., Canada, T6G 2E8;Department of Computing Science, University of Alberta, Edmonton, Alta., Canada, T6G 2E8

  • Venue:
  • Discrete Applied Mathematics
  • Year:
  • 2005

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Abstract

Let C"n","m^2^,^k^,^t be a random constraint satisfaction problem (CSP) on n binary variables, where m constraints are selected uniformly at random from all the possible k-ary constraints each of which contains exactly t tuples of the values as its restrictions. We establish an upper bound on the constraint tightness threshold for C"n","m^2^,^k^,^t to have an exponential resolution complexity. The upper bound partly answers the open problem regarding the CSP resolution complexity with the tightness between the existing upper and lower bounds [D. Mitchell, Resolution complexity of random constraints, in: Proceedings Principles and Practices of Constraint Programming-CP 2002, Springer, Berlin, 2002, pp. 295-309].