  Due to the limitation on computational power of existing computers, the
polynomial time does not works for identifying the tractable problems in big
data computing. This paper adopts the sublinear time as the new tractable
standard to recognize the tractability in big data computing, and the
random-access Turing machine is used as the computational model to characterize
the problems that are tractable on big data. First, two pure-tractable classes
are first proposed. One is the class $\mathrm{PL}$ consisting of the problems
that can be solved in polylogarithmic time by a RATM. The another one is the
class $\mathrm{ST}$ including all the problems that can be solved in sublinear
time by a RATM. The structure of the two pure-tractable classes is deeply
investigated and they are proved $\mathrm{PL^i} \subsetneq \mathrm{PL^{i+1}}$
and $\mathrm{PL} \subsetneq \mathrm{ST}$. Then, two pseudo-tractable classes,
$\mathrm{PTR}$ and $\mathrm{PTE}$, are proposed. $\mathrm{PTR}$ consists of all
the problems that can solved by a RATM in sublinear time after a PTIME
preprocessing by reducing the size of input dataset. $\mathrm{PTE}$ includes
all the problems that can solved by a RATM in sublinear time after a PTIME
preprocessing by extending the size of input dataset. The relations among the
two pseudo-tractable classes and other complexity classes are investigated and
they are proved that $\mathrm{PT} \subseteq \mathrm{P}$, $\sqcap'\mathrm{T^0_Q}
\subsetneq \mathrm{PTR^0_Q}$ and $\mathrm{PT_P} = \mathrm{P}$.
