In this paper, we propose an arc-search corrector-predictor
interior-point method for solving $P_*(kappa)$-linear
complementarity problems. The proposed algorithm searches the
optimizers along an ellipse that is an approximation of the central
path. The algorithm generates a sequence of iterates in the wide
neighborhood of central path introduced by Ai and Zhang. The
algorithm does not depend on the handicap $kappa$ of the problem,
so that it can be used for any $P_*(kappa)$-linear complementarity
problem. Based on the ellipse approximation of the central path and
the wide neighborhood, we show that the proposed algorithm has
$O((1+kappa)sqrt{n}L)$ iteration complexity, the best-known
iteration complexity obtained so far by any interior-point method
for solving $P_*(kappa)$-linear complementarity problems.