  Epistemic logic programs (ELPs) are a popular generalization of standard
Answer Set Programming (ASP) providing means for reasoning over answer sets
within the language. This richer formalism comes at the price of higher
computational complexity reaching up to the fourth level of the polynomial
hierarchy. However, in contrast to standard ASP, dedicated investigations
towards tractability have not been undertaken yet. In this paper, we give first
results in this direction and show that central ELP problems can be solved in
linear time for ELPs exhibiting structural properties in terms of bounded
treewidth. We also provide a full dynamic programming algorithm that adheres to
these bounds. Finally, we show that applying treewidth to a novel dependency
structure---given in terms of epistemic literals---allows to bound the number
of ASP solver calls in typical ELP solving procedures.
