  This paper introduces a special family of randomized algorithms for Max DICUT
that we call oblivious algorithms. Let the bias of a vertex be the ratio
between the total weight of its outgoing edges and the total weight of all its
edges. An oblivious algorithm selects at random in which side of the cut to
place a vertex v, with probability that only depends on the bias of v,
independently of other vertices. The reader may observe that the algorithm that
ignores the bias and chooses each side with probability 1/2 has an
approximation ratio of 1/4, whereas no oblivious algorithm can have an
approximation ratio better than 1/2 (with an even directed cycle serving as a
negative example). We attempt to characterize the best approximation ratio
achievable by oblivious algorithms, and present results that are nearly tight.
The paper also discusses natural extensions of the notion of oblivious
algorithms, and extensions to the more general problem of Max 2-AND.
