最短公共超串与基因组组装计算复杂性中的相变
Phase transition in the computational complexity of the shortest common superstring and genome assembly
AI总结：
本文利用统计力学揭示最短公共超串与基因组组装问题的计算复杂性存在相变，解释实际大规模实例为何易解，并提出在困难区域更优的 MCMC 方法。
摘要：
基因组组装是通过比对并合并短片段（即 reads，读段）来重建长遗传序列的过程；无论是作为最短公共超串问题的一个版本，还是以 Hamiltonian 回路形式表述，它都被公认为 NP-hard。也就是说，在最坏情况下，计算时间被认为会随问题规模呈指数增长。尽管如此，高通量技术和现代算法目前已使生物信息学家能够处理包含数十亿条读段的数据集。我们运用统计力学方法来解释这一矛盾，证明该问题的计算复杂性存在相变，并表明实际实例总是处于“容易”相（可由多项式时间算法求解）。此外，我们提出一种 Markov-chain Monte Carlo 方法，在困难区域优于常见的确定性算法。
英文摘要：
Genome assembly, the process of reconstructing a long genetic sequence by aligning and merging short fragments, or reads, is known to be NP-hard, either as a version of the shortest common superstring problem or in a Hamiltonian-cycle formulation. That is, the computing time is believed to grow exponentially with the the problem size in the worst case. Despite this fact, high-throughput technologies and modern algorithms currently allow bioinformaticians to handle datasets of billions of reads. Using methods from statistical mechanics, we address this conundrum by demonstrating the existence of a phase transition in the computational complexity of the problem and showing that practical instances always fall in the 'easy' phase (solvable by polynomial-time algorithms). In addition, we propose a Markov-chain Monte Carlo method that outperforms common deterministic algorithms in the hard regime.
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