## Abstract

We formalize and examine the online Dictionary Recognition with One Gap problem (DROG) which is the following. Preprocess a dictionary D of d patterns, where each pattern contains a special gap symbol that can match any string, so that given a text that arrives online, a character at a time, we can report all the patterns from D that have not been reported yet and are suffixes of the text that has arrived so far, before the next character arrives. The gap symbols are associated with bounds determining the possible lengths of matching strings. Online DROG captures the difficulty in a bottleneck procedure for cyber-security, as many digital signatures of viruses manifest themselves as patterns with a single gap. Following the work of [4] on the closely related online Dictionary Matching with One Gap problem (DMOG), we provide algorithms whose time cost depends linearly on δ(G_{D}), where G_{D} is a bipartite graph that captures the structure of D and δ(G_{D}) is the degeneracy of this graph. These algorithms are of practical interest since although δ(G_{D}) can be as large as ^{√}d, and even larger if G_{D} is a multi-graph, it is typically a very small constant in practice. Finally, when δ(G_{D}) is large we describe other efficient solutions.

Original language | English |
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Title of host publication | Proceedings of the Prague Stringology Conference, PSC 2017 |

Editors | Jan Holub, Jan Zdarek |

Publisher | Prague Stringology Club |

Pages | 3-17 |

Number of pages | 15 |

ISBN (Electronic) | 9788001061930 |

State | Published - 2017 |

Event | 21st Prague Stringology Conference, PSC 2017 - Prague, Czech Republic Duration: 28 Aug 2017 → 30 Aug 2017 |

### Publication series

Name | Proceedings of the Prague Stringology Conference, PSC 2017 |
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### Conference

Conference | 21st Prague Stringology Conference, PSC 2017 |
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Country/Territory | Czech Republic |

City | Prague |

Period | 28/08/17 → 30/08/17 |

### Bibliographical note

Publisher Copyright:© Czech Technical University in Prague, Czech Republic.