Before revision:  When the item space is the unit interval 0,1 and buyers have piecewise linear utilities , we show that \epsilon-approximate equilibrium prices can be computed in time polynomial in the market size and \log \frac{1{\epsilon}.
After revision:  When the item space is the unit interval 0,1 and buyers have piecewise linear valuations , we show that \epsilon-approximate equilibrium prices can be computed in time polynomial in the market size and \log \frac{1{\epsilon}.