arXiv subjects

Maria Constantin

Publications and source records attributed to Maria Constantin.

2 recordsLinked to original sources

arXiv2026

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

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.

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arXiv2026

Complexity and Algorithms for Unary Translocation Distance

Given a finite set of integers $A$, a \emph{unary translocation} produces a new set $A' = A \cup \{u,v\}$, where $u$ and $v$ are nonnegative integers satisfying $x+y=u+v$ for some $x,y\in A$. For an input set $A$ and a target set $B$, the \emph{unary translocation distance} is the minimum number of unary translocations required to obtain a superset containing $B$. In this paper, we study this problem from both theoretical and computational perspectives. We prove that computing the unary translocation distance is strongly NP-hard, thereby answering an open question raised by \citet{ConstantinMiclausPopa2026UnaryTranslocation}. On the positive side, we give an exact pseudo-polynomial algorithm for every fixed constant value of $|B|$, extending our previous results for $|B|\leq 2$. For arbitrary target sets, we present a $2$-approximation algorithm, an additive $(|B|-1)$-approximation algorithm, and show that the additive algorithm also yields a $3$-approximation. We also propose parameterized algorithms, including algorithms parameterized by the maximum value in the input set together with the optimum distance, and by the maximum value in the target set together with $|B|$. In addition, we propose an integer linear programming formulation that gives an exact mathematical model for the problem, analyze its size, and show that the LP relaxation has integrality gap at least $\frac{4}{3}$. Finally, we report computational experiments comparing the $2$-approximation algorithm, beam search, and simulated annealing. The results show that the approximation algorithm is highly effective in practice and often outperforms the heuristic baselines.

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