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OBDD-based graph algorithms deal with the characteristic function of the edgeset E of a graph $G = (V,E)$ which is represented by an OBDD and solveoptimization problems by mainly using functional operations. We present anOBDD-based algorithm which uses randomization for the first time. Inparticular, we give a maximal matching algorithm with $O(\log^3 \vert V \vert)$functional operations in expectation. This algorithm may be of independentinterest. The experimental evaluation shows that this algorithm outperformsknown OBDD-based algorithms for the maximal matching problem.  In order to use randomization, we investigate the OBDD complexity of $2^n$(almost) $k$-wise independent binary random variables. We give a OBDDconstruction of size $O(n)$ for $3$-wise independent random variables and showa lower bound of $2^{\Omega(n)}$ on the OBDD size for $k \geq 4$. The bestknown lower bound was $\Omega(2^n/n)$ for $k \approx \log n$ due to Kabanets.We also give a very simple construction of $2^n$ $(\varepsilon, k)$-wiseindependent binary random variables by constructing a random OBDD of width $O(nk^2/\varepsilon)$.

OBDDs and (Almost) $k$-wise Independent Random Variables