## Abstract

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(n^{2} /log^{2} 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 n^{O(w)} algorithm.

Original language | English GB |
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Pages (from-to) | 517-528 |

Number of pages | 12 |

Journal | Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) |

DOIs | |

State | Published - 24 Sep 2013 |

Event | 21st Annual European Symposium on Algorithms, ESA 2013 - Sophia Antipolis, France Duration: 2 Sep 2013 → 4 Sep 2013 |

## ASJC Scopus subject areas

- Theoretical Computer Science
- Computer Science (all)