提出新数据结构与并行算法，高效计数精确覆盖问题解。
A Parallel Approach to Counting Exact Covers Based on Decomposability Property
- 用决策型可分解否定正则形式压缩表示精确覆盖解集。
- 新算法在多个数据集上速度比现有方法快数倍。
- 适合处理大规模组合优化问题的研究者参考。
精确覆盖问题是人工智能领域中经典的NP难问题，具有广泛的应用。算法DXZ利用零抑制二叉决策图（ZBDDs）来表示精确覆盖的解集。本文提出一种零抑制型决策可分解否定正则形式（decision-ZDNNF），其表示能力严格优于ZBDDs。我们设计了一种新的并行算法DXD，用于构建代表所有精确覆盖解的decision-ZDNNF。此外，通过动态更新连通分量进一步优化了DXD。实验结果表明，改进后的DXD算法在性能上全面超越当前最先进的方法。
原文摘要 · Abstract (English)
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.
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