  This paper considers the multi-parametric linear complementarity problem
(pLCP) with sufficient matrices. The main result is an algorithm to find a
polyhedral decomposition of the set of feasible parameters and to construct a
piecewise affine function that maps each feasible parameter to a solution of
the associated LCP in such a way that the function is affine over each cell of
the decomposition. The algorithm is output-sensive in the sense that its time
complexity is polynomial in the size of the input and linear in the size of the
output, when the problem is non-degenerate. We give a lexicographic
perturbation technique to resolve degeneracy as well. Unlike for the
non-parametric case, the resolution turns out to be nontrivial, and in
particular, it involves linear programming (LP) duality and multi-objective LP.
