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arXiv · 2507.19139

String Consensus Problems with Swaps and Substitutions

Estéban Gabory·Laurent Bulteau·Gabriele Fici·Hilde Verbeek
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Abstract

String consensus problems aim at finding a string that minimizes some given distance with respect to an input set of strings. In particular, in the Closest string problem, we are given a set of strings of equal length and a radius $d$. The objective is to find a new string that differs from each input string by at most $d$ substitutions. We study a generalization of this problem where, in addition to substitutions, swaps of adjacent characters are also permitted, each operation incurring a unit cost. Amir et al. showed that this generalized problem is NP-hard, even when only swaps are allowed. In this paper, we show that it is FPT with respect to the parameter $d$. Moreover, we investigate a variant in which the goal is to minimize the sum of distances from the output string to all input strings. For this version, we present a polynomial-time algorithm.

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Estéban Gabory, Laurent Bulteau, Gabriele Fici, Hilde Verbeek. 2025-07-25. String Consensus Problems with Swaps and Substitutions. https://arxiv.org/abs/2507.19139

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