Binary jumbled pattern matching on trees and tree-like structures

Travis Gagie, Danny Hermelin, Gad M. Landau, Oren Weimann

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


Binary jumbled pattern matching asks to preprocess a binary string S in order to answer queries (i,j) which ask for a substring of S that is of length i and has exactly j 1-bits. This problem naturally generalizes to vertex-labeled trees and graphs by replacing "substring" with "connected subgraph". In this paper, we give an O(n2 /log2 n)-time solution for trees, matching the currently best bound for (the simpler problem of) strings. We also give an O(g 2/3 n 4/3/(logn) 4/3)-time solution for strings that are compressed by a grammar of size g. This solution improves the known bounds when the string is compressible under many popular compression schemes. Finally, we prove that the problem is fixed-parameter tractable with respect to the treewidth w of the graph, even for a constant number of different vertex-labels, thus improving the previous best nO(w) algorithm.

Original languageEnglish
Title of host publicationAlgorithms, ESA 2013 - 21st Annual European Symposium, Proceedings
Number of pages12
StatePublished - 2013
Event21st Annual European Symposium on Algorithms, ESA 2013 - Sophia Antipolis, France
Duration: 2 Sep 20134 Sep 2013

Publication series

NameLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume8125 LNCS
ISSN (Print)0302-9743
ISSN (Electronic)1611-3349


Conference21st Annual European Symposium on Algorithms, ESA 2013
CitySophia Antipolis

ASJC Scopus subject areas

  • Theoretical Computer Science
  • General Computer Science


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