NP-Hardness and a Fixed-Parameter Algorithm for Translocation Distance

2026-09-16

AI Summary

本文研究了通过转位事件进行的基因组重排问题，证明了非均匀连续和非均匀非连续转位距离问题是NP难问题，并为特定情况提供了一个固定参数算法。

Abstract

In this paper we study the genome rearrangements done by translocation events. Genome rearrangements were used to measure evolutionary distance between organisms since 1936 (Dobzhansky and Sturtevant). The chromosomes are represented as strings of DNA and the \emph{translocation operation} is defined as the exchange of prefixes between two strings. This operation results in the creation of two new strings (chromosomes) that can then be utilized in subsequent translocations. A translocation is referred to as \emph{contiguous} if the new strings are produced in a single copy, so each of them can be used in only one subsequent operation. When the words produced by a translocation operation are considered to have an infinite number of copies, the translocation is referred to as \emph{non-contiguous}. If the exchanged prefixes are of equal length, the translocation is called \emph{uniform}. Otherwise, the translocation is termed \emph{non-uniform}. The \emph{translocation distance} between two sets of strings, termed the input set and the target set, represents the minimum number of translocations necessary to obtain all the strings in the target set via translocation operations. We prove that both the non-uniform contiguous and the non-uniform non-contiguous translocation distance problems are NP-hard over arbitrary finite alphabets, where the alphabet is part of the input. For the case in which the target set consists of a single string, we give a fixed-parameter tractable algorithm parameterized by the length of the target string.

Problem

• translocation distance
• genome rearrangements
• NP-hardness

Innovation

• non-uniform translocation
• NP-hardness
• fixed-parameter tractable algorithm