非均匀非连续易位距离的近似算法
An Approximation Algorithm for Non-uniform Non-contiguous Translocation Distance
- University of Bucharest（布加勒斯特大学）
- National Institute for Research and Development in Informatics（罗马尼亚信息学研究与开发国家研究所）
机构由 AI 辅助整理，请以论文原文为准。
中文总结 AI 辅助
针对非均匀非连续易位距离问题，提出首个多项式时间近似算法，对单个目标串达到O(log n)近似比，对任意有限目标集达到O(log N)近似比，解决了开放问题。
中文摘要 AI 辅助
易位是交换两条染色体前缀的基因组重排操作。我们研究非均匀非连续易位距离问题，其中计算过程中产生的每个字符串都保持可用以供重用。给定初始字符串集合$A$和目标集合$B$，目标是用尽可能少的易位操作生成$B$中的所有字符串。我们提出了该问题的第一个多项式时间近似算法。对于长度为$n$的单个目标字符串，我们获得$O(\log n)$近似比，并将结果扩展到任意有限目标集合，获得$O(\log N)$近似比，其中$N$是初始集合中尚未存在的目标的总长度。这解决了Constantin和Popa（TCS 2025）留下的非均匀非连续情形的可近似性问题。
英文摘要
Translocations are genome rearrangement operations that exchange prefixes of two chromosomes. We study the non-uniform non-contiguous translocation distance problem, where every string produced during the computation remains available for reuse. Given an initial set of strings $A$ and a target set $B$, the objective is to produce all strings in $B$ using as few translocations as possible. We present the first polynomial-time approximation algorithm for this problem. For a single target string of length $n$, we obtain an $O(\log n)$-approximation, and we extend the result to arbitrary finite target sets with an $O(\log N)$-approximation, where $N$ is the total length of the targets not already present in the initial set. This resolves the approximability question for the non-uniform non-contiguous case left open by Constantin and Popa (TCS 2025).
