The communication complexity of interval orders

The communication complexity of interval orders is studied within the following model. Two players choose two elements x and y and want to determine whether x<y holds by exchanging as few bits of information as possible. It is shown that an optimal one-way protocol exists by first establishing a rank-optimality result for a subclass of generalized interval orders. It turns out that the deterministic and nondeterministic communication complexities coincide for generalized interval orders. The analogous statement for the complementary relation is true for interval orders in the strict sense while it need not hold for generalized interval orders.