Tags:Multi-Pass Dynamic Programming, Parameterized Algorithms, Projected Model Counting, Propositional Logic and Tree Decompositions

Abstract:

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 bounded primal or incidence treewidth 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, which yields that runtime bounds of our algorithm are tight.

Exploiting Treewidth for Projected Model Counting and its Limits