English

A Parallel Approach to Counting Exact Covers Based on Decomposability Property

Artificial Intelligence 2026-04-17 v1

Abstract

The exact cover problem is a classical NP-hard problem with broad applications in the area of AI. Algorithm DXZ is a method to count exact covers representing by zero-suppressed binary decision diagrams (ZBDDs). In this paper, we propose a zero-suppressed variant of decision decomposable negation normal form (in short, decision-ZDNNF), which is strictly more succinct than ZBDDs. We then design a novel parallel algorithm, namely DXD, which constructs a decision-ZDNNF representing the set of all exact covers. Furthermore, we improve DXD by dynamically updating connected components. The experimental results demonstrate that the improved DXD algorithm outperforms all of state-of-the-art methods.

Keywords

Cite

@article{arxiv.2604.14627,
  title  = {A Parallel Approach to Counting Exact Covers Based on Decomposability Property},
  author = {Liangda Fang and Yaohui Luo and Delong Li and Xuanxiang Huang and Quanlong Guan},
  journal= {arXiv preprint arXiv:2604.14627},
  year   = {2026}
}

Comments

Submitted to SAT 2026

R2 v1 2026-07-01T12:12:01.461Z