Before revision:   ]  ]  Our algorithms are based on the idea of using recursion as in Savitch's theorem \mbox{%DIFAUXCMD \cite{Savitch70}\hspace{0pt}%DIFAUXCMD }  , and a careful modification of previous techniques to make the recursion work.
After revision:  Furthermore, our results can be used to improve a recent result by Farhadi et. al. ] ] Our algorithms are based on the idea of using recursion as in Savitch's theorem \mbox{%DIFAUXCMD \cite{Savitch70}\hspace{0pt}%DIFAUXCMD } , and a careful modification of previous techniques to make the recursion work.