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We show that Van der Heyden's variable dimension algorithm and Dantzig and Cottle's principal pivoting method require 2n–1 pivot steps to solve a class of linear complementarity problems of ordern. Murty and Fathi have previously shown that the computational effort required to solve a linear complementarity problem of ordern by Lemke's complementary pivot algorithm or by Murty's Bard-type algorithm is not bounded above by a polynomial inn. Our study shows that the variable dimension algorithm and the principal pivoting method have similar worst case computational requirements.

Computational complexity of Van der Heyden's variable dimension algorithm and Dantzig-Cottle's principal pivoting method for solving LCP's