License: Creative Commons Attribution 4.0 International license (CC BY 4.0)
When quoting this document, please refer to the following
DOI: 10.4230/LIPIcs.CPM.2021.24
URN: urn:nbn:de:0030-drops-139759
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Sobel, Joshua ; Bertram, Noah ; Ding, Chen ; Nargesian, Fatemeh ; Gildea, Daniel

AWLCO: All-Window Length Co-Occurrence

LIPIcs-CPM-2021-24.pdf (1 MB)


Analyzing patterns in a sequence of events has applications in text analysis, computer programming, and genomics research. In this paper, we consider the all-window-length analysis model which analyzes a sequence of events with respect to windows of all lengths. We study the exact co-occurrence counting problem for the all-window-length analysis model. Our first algorithm is an offline algorithm that counts all-window-length co-occurrences by performing multiple passes over a sequence and computing single-window-length co-occurrences. This algorithm has the time complexity O(n) for each window length and thus a total complexity of O(n²) and the space complexity O(|I|) for a sequence of size n and an itemset of size |I|. We propose AWLCO, an online algorithm that computes all-window-length co-occurrences in a single pass with the time complexity of O(n) and space complexity of O(√{n|I|}), assuming perfect hashing. Following this, we generalize our use case to patterns in which we propose an algorithm that computes all-window-length co-occurrence with time complexity O(n|I|), assuming perfect hashing, with an additional pre-processing step and space complexity O(√{n|I|}+|I|), plus the overhead of the Aho-Corasick algorithm [Aho and Corasick, 1975].

BibTeX - Entry

  author =	{Sobel, Joshua and Bertram, Noah and Ding, Chen and Nargesian, Fatemeh and Gildea, Daniel},
  title =	{{AWLCO: All-Window Length Co-Occurrence}},
  booktitle =	{32nd Annual Symposium on Combinatorial Pattern Matching (CPM 2021)},
  pages =	{24:1--24:21},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-186-3},
  ISSN =	{1868-8969},
  year =	{2021},
  volume =	{191},
  editor =	{Gawrychowski, Pawe{\l} and Starikovskaya, Tatiana},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{},
  URN =		{urn:nbn:de:0030-drops-139759},
  doi =		{10.4230/LIPIcs.CPM.2021.24},
  annote =	{Keywords: Itemsets, Data Sequences, Co-occurrence}

Keywords: Itemsets, Data Sequences, Co-occurrence
Collection: 32nd Annual Symposium on Combinatorial Pattern Matching (CPM 2021)
Issue Date: 2021
Date of publication: 30.06.2021

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