Exploiting Treewidth for Projected Model Counting and its Limits
  In this paper, we introduce a novel algorithm to solve projected model
counting (PMC). PMC asks to count solutions of a Boolean formula with respect
to a given set of projected variables, where multiple solutions that are
identical when restricted to the projected variables count as only one
solution. Our algorithm exploits small treewidth of the primal graph of the
input instance. It runs in time $O({2^{2^{k+4}} n^2})$ where k is the treewidth
and n is the input size of the instance. In other words, we obtain that the
problem PMC is fixed-parameter tractable when parameterized by treewidth.
Further, we take the exponential time hypothesis (ETH) into consideration and
establish lower bounds of bounded treewidth algorithms for PMC, yielding
asymptotically tight runtime bounds of our algorithm.
