# Exploiting Treewidth for Projected Model Counting and its Limits

arXiv: https://arxiv.org/abs/1805.05445 · HTML: https://mlsanity.com/paper/1805.05445/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 14 May 2018.

## Built on by (most cited first, 2 of 2)

- [Treewidth-aware Reductions of Normal ASP to SAT -- Is Normal ASP Harder than SAT after All?](https://mlsanity.com/paper/2210.03553/) (2022)
- [Solving Projected Model Counting by Utilizing Treewidth and its Limits](https://mlsanity.com/paper/2305.19212/) (2023)

## Abstract (arXiv)

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(2^2k+4 n2) 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.