Reconstructing General Matching Graphs

Amihood Amir, Michael Itzhaki

Research output: Chapter in Book/Report/Conference proceedingConference contributionpeer-review


The classical pattern matching paradigm is that of seeking occurrences of one string in another, where both strings are drawn from an alphabet set Σ. Motivated by many applications, algorithms were developed for pattern matching where the matching relation is not necessarily the “=” relation. Examples are pattern matching with “don’t cares”, approximate matching, less-than matching, Cartesian-tree matching, order preserving matching, parameterized matching, degenerate matching, function matching, and more. Some of the matchings above allow for efficient pattern matching algorithms, while others do not. Much work has not been done on categorization of the complexity of various string matching queries based on the type of matching. For example, when can exact matching be done fast? When can approximate matching be calculated fast? When can tandem or palindrome recognition be efficiently calculated? This paper defines the matching graph of a given string under a matching relation. We show that the type of graph affects various string algorithms. The matching graph can also be a tool for lower bounds. We provide a lower bound for finding palindromes in a general degenerate graph. We also show some results in recognizing the minimum alphabet required for reconstructing a string that presents a given matching graph.

Original languageEnglish
Title of host publication35th Annual Symposium on Combinatorial Pattern Matching, CPM 2024
EditorsShunsuke Inenaga, Simon J. Puglisi
PublisherSchloss Dagstuhl- Leibniz-Zentrum fur Informatik GmbH, Dagstuhl Publishing
ISBN (Electronic)9783959773263
StatePublished - Jun 2024
Event35th Annual Symposium on Combinatorial Pattern Matching, CPM 2024 - Fukuoka, Japan
Duration: 25 Jun 202427 Jun 2024

Publication series

NameLeibniz International Proceedings in Informatics, LIPIcs
ISSN (Print)1868-8969


Conference35th Annual Symposium on Combinatorial Pattern Matching, CPM 2024

Bibliographical note

Publisher Copyright:
© Amihood Amir and Michael Itzhaki.


  • Matching Graphs
  • NP-hardness
  • Pattern Matching
  • Reconstruction


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