the constraints, using a solver for constraint-satisfaction problems. But if the domain is large, the above approach becomes unfeasible due to the large number of possible values that this function can have: , where m is the number of different values in the domain, and n is the number of variables. Bouveret and Lemaître present five different algorithms for finding leximin-optimal solutions to discrete constraint-satisfaction problems: Branch and bound based on the LEXIMIN constraint - a constraint on two vectors x and y, saying that y is leximin-larger than x. Branching on saturated subsets - finding subsets of variables that must be fixed at the minimum value, and finding the maximum-minimum value for the other variables. Using the SORT constraint - a constraint on two vectors x and y, saying that y contains the same elements as x sorted in ascending order. This constraint can be computed efficiently by several algorithms. Using the ATLEAST constraint. Using max-min transformations. In their experiments, the best-performing approach was 4 (ATLEAST), followed by 3 (SORT) followed by 1 (LEXIMIN). Dall'aglio presents an algorithm for computing a leximin-optimal resource allocation. See also In game theory, the nucleolus is defined as a lexicographically minimal solution set. References Multiple-criteria decision analysis Optimization algorithms and methods