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}
}
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