Binary jumbled pattern matching on trees and tree-like structures

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

Research output: Contribution to journalConference articlepeer-review

13 Scopus citations


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 GB
Pages (from-to)517-528
Number of pages12
JournalLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
StatePublished - 24 Sep 2013
Event21st Annual European Symposium on Algorithms, ESA 2013 - Sophia Antipolis, France
Duration: 2 Sep 20134 Sep 2013

ASJC Scopus subject areas

  • Theoretical Computer Science
  • Computer Science (all)


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