Matching Patterns with Variables under Hamming Distance

  title={Matching Patterns with Variables under Hamming Distance},
  author={Pawel Gawrychowski and Florin Manea and Stefan Siemer},
A pattern α is a string of variables and terminal letters. We say that α matches a word w, consisting only of terminal letters, if w can be obtained by replacing the variables of α by terminal words. The matching problem, i.e., deciding whether a given pattern matches a given word, was heavily investigated: it is NP-complete in general, but can be solved efficiently for classes of patterns with restricted structure. In this paper, we approach this problem in a generalized setting, by… Expand

Tables from this paper


A note on the complexity of matching patterns with variables
  • M. Schmid
  • Mathematics, Computer Science
  • Inf. Process. Lett.
  • 2013
This work shows that the problem of matching patterns with variables remains NP-complete even if every variable has at most two occurrences, and shows that if patterns can be represented as special kinds of planar graphs, then they can be matched in polynomial time. Expand
Local Patterns
Two new classes of patterns are presented, called k-local, and stronglynested, and it is shown that the respective matching problems, as well as membership can be solved efficiently for any fixed k. Expand
Matching Patterns with Variables
A series of recent results related to efficient matching for patterns with variables, as well as a series of extensions of this problem are overviewed. Expand
Pattern Matching with Variables: A Multivariate Complexity Analysis
This work considers numerous parameters of this problem and investigates the question whether or not the variant obtained by bounding these parameters by constants can be solved ef fi ciently. Expand
Which Regular Expression Patterns Are Hard to Match?
  • A. Backurs, P. Indyk
  • Mathematics, Computer Science
  • 2016 IEEE 57th Annual Symposium on Foundations of Computer Science (FOCS)
  • 2016
It is shown that the complexity of regular expression matching can be characterized based on its depth (when interpreted as a formula), and that all problems can either be solved in strongly sub-quadratic time, or cannot be solve in stronglySub-quadriatic time assuming the Strong Exponential Time Hypothesis. Expand
Approximate matching of regular expressions.
An algorithm to solve the problem in time O(MN), where M and N are the lengths of A and R, and requires only O(N) space to deliver just the score of the best alignment, superior to an earlier algorithm by Wagner and Seiferas. Expand
A Parameterized Study of Maximum Generalized Pattern Matching Problems
This paper studies the parameterized complexity of the optimization variant of GFM (called Max-GFM), which has been introduced in Amir and Amihood and is allowed to replace some of the pattern letters with some special symbols “?”, termed wildcards or don’t cares, which can be mapped to an arbitrary substring of the text. Expand
Finding Patterns Common to a Set of Strings
  • D. Angluin
  • Computer Science, Mathematics
  • J. Comput. Syst. Sci.
  • 1980
The main result is a polynomial-time algorithm for the special case of patterns containing only one variable symbol (possibly occurring several times in the pattern). Expand
Towards Unified Approximate Pattern Matching for Hamming and L_1 Distance
A smooth time trade-off is provided by exhibiting an O~((m+k sqrt{m})* n/m) time algorithm, and a matching conditional lower bound is added, showing that a significantly faster combinatorial algorithm is not possible, unless the combinatorially matrix multiplication conjecture fails. Expand
Efficient string matching in the presence of errors
  • G. Landau, U. Vishkin
  • Computer Science
  • 26th Annual Symposium on Foundations of Computer Science (sfcs 1985)
  • 1985
An algorithm for finding all occurrences of the pattern in the text, each with at most k mismatches (superfluous characters in either the text or the pattern are not allowed), which runs in O(k(m logm + n)) time. Expand