  We present the constrained Monte Carlo (CMC) algorithm for the QCD evolution.
The constraint resides in that the total longitudinal energy of the emissions
in the MC and in the underlying QCD evolution is predefined (constrained). This
CMC implements exactly the full DGLAP evolution of the parton distributions in
the hadron with respect to the logarithm of the energy scale. The algorithm of
the CMC is referred to as the non-Markovian type. The non-Markovian MC
algorithm is defined as the one in which the multiplicity of emissions is
chosen randomly as the first variable and not the last one, as in the Markovian
MC algorithms. The former case resembles that of the fixed-order matrix element
calculations. The CMC algorithm can serve as an alternative to the so-called
backward evolution Markovian algorithm of Sjostrand, which is used for
modelling the initial-state parton shower in modern QCD MC event generators. We
test practical feasibility and efficiency of our CMC implementation in a series
of numerical exercises, comparing its results with those from other MC and
non-MC programs, in a wide range of Q and x, down to the 0.1% precision level.
In particular, satisfactory numerical agreement is found with the results of
the Markovian MC program of our own and the other non-MC program. The
efficiency of the new constrained MC is found to be quite good.
