An Approximation Algorithm for Non-uniform Non-contiguous Translocation Distance

2026-09-21

AI Summary

本文解决了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，对单一目标字符串长度n获得O(log n)近似比，并推广至任意有限目标集。

Abstract

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).

Problem

• non-uniform
• non-contiguous
• translocation distance

Innovation

• non-uniform non-contiguous translocation
• polynomial-time approximation algorithm
• O(log n)-approximation