  Based on our previous work to the reduced Ostrovsky equation (J. Phys. A 45
355203), we construct its integrable semi-discretizations. Since the reduced
Ostrovsky equation admits two alternative representations, one is its original
form, the other is the differentiation form, or the short wave limit of the
Degasperis-Procesi equation, two semi- discrete analogues of the reduced
Ostrovsky equation are constructed possessing the same N-loop soliton solution.
The relationship between these two versions of semi-discretizations is also
clarified.
