Parameterized Complexity Analysis for the Closest String with Wildcards Problem

Dan Hermelin, Liat Rozenberg

Research output: Chapter in Book/Report/Conference proceedingEntry for encyclopedia/dictionarypeer-review


The Closest String problem asks to find a string s which is not too far from each string in a set of m input strings, where the distance is taken as the Hamming distance. This well-studied problem has various applications in computational biology and drug design. In this paper, we introduce a new variant of Closest String where the input strings can contain wildcards that can match any letter in the alphabet, and the goal is to find a solution string without wildcards. We call this problem the Closest String with Wildcards problem, and we analyze it in the framework of parameterized complexity. Our study determines for each natural parameterization whether this parameterization yields a fixed-parameter algorithm, or whether such an algorithm is highly unlikely to exist. More specifically, let m denote the number of input strings, each of length n, and let d be the given distance bound for the solution string. Furthermore, let k denote the minimum number of wildcards in any input string. We present fixed-parameter algorithms for the parameters m, n, and k+d, respectively. On the other hand, we then show that such results are unlikely to exist when k and d are taken as single parameters. This is done by showing that the problem is NP-hard already for k=0 and d ≥2. Finally, to complement the latter result, we present a polynomial-time algorithm for the case of d=1. Apart from this last result, all other results hold even when the strings are over a general alphabet.

Original languageAmerican English
Title of host publicationCombinatorial Pattern Matching
Subtitle of host publication25th Annual Symposium, CPM 2014, Proceedings
EditorsAlexander S. Kulikov, Sergei O. Kuznetsov, Pavel Pevzner
Number of pages10
ISBN (Print)978-3-319-07566-2
StatePublished - Jan 2014
Event25th Annual Symposium on Combinatorial Pattern Matching, CPM 2014 - Moscow, Russian Federation
Duration: 16 Jun 201418 Jun 2014

Publication series

NameLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
PublisherSpringer Verlag


Conference25th Annual Symposium on Combinatorial Pattern Matching, CPM 2014
Country/TerritoryRussian Federation

All Science Journal Classification (ASJC) codes

  • Theoretical Computer Science
  • General Computer Science


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