Binary constraint

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A binary constraint, in mathematical optimization, is a constraint that involves exactly two variables.

For example, consider the n-queens problem, where the goal is to place n chess queens on an n-by-n chessboard such that none of the queens can attack each other (horizontally, vertically, or diagonally). The formal set of constraints are therefore "Queen 1 can't attack Queen 2", "Queen 1 can't attack Queen 3", and so on between all pairs of queens. Each constraint in this problem is binary, in that it only considers the placement of two individual queens. [1]

Linear programs in which all constraints are binary can be solved in strongly polynomial time, a result that is not known to be true for more general linear programs. [2]

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References

  1. Marriott, Kim; Stuckey, Peter J. (1998), Programming with Constraints: An Introduction, MIT Press, p. 282, ISBN   9780262133418 .
  2. Megiddo, Nimrod (1983), "Towards a genuinely polynomial algorithm for linear programming", SIAM Journal on Computing , 12 (2): 347–353, CiteSeerX   10.1.1.76.5 , doi:10.1137/0212022, MR   0697165 .