Approximating layout problems on random graphs

We show that, with overwhelming probability, several well-known layout problems are approximable within a constant for random graphs drawn from the G(n, p(n)) model where C/n less than or equal to p(n) less than or equal to 1 for all n big enough and for some properly characterized parameter C > 1. In fact, our results establish that, with overwhelming probability, the cost of any arbitrary layout of such a random graph is within a constant of the optimal cost. (C) 2001 Elsevier Science B.V. All rights reserved.