The problem of reconstructing a sequence of independent and identically distributed symbols from a set of equal size, consecutive, fragments, as well as a dependent reference sequence, is considered. First, in the regime in which the fragments are relatively long, and typically no fragment appears more than once, the scaling of the failure probability of maximum likelihood reconstruction algorithm is exactly determined for perfect reconstruction and bounded for partial reconstruction. Second, the regime in which the fragments are relatively short and repeating fragments abound is characterized. A trade-off is stated between the fraction of fragments that cannot be adequately reconstructed vs. the distortion level allowed for the reconstruction of each fragment, while still allowing vanishing failure probability

翻译：考虑从一组等长、连续的片段以及一个相关的参考序列中重构独立同分布符号序列的问题。首先，在片段相对较长且通常没有片段出现多于一次的情况下，精确确定了完美重构下最大似然重构算法失败概率的缩放规律，并给出了部分重构下的界限。其次，刻画了片段相对较短且重复片段大量存在的场景。在允许每片段重构失真水平的同时，无法充分重构的片段比例与仍需保证失败概率趋近于零之间存在权衡关系。