Space lower bounds for online pattern matching

Raphaël Clifford, Markus Jalsenius, Ely Porat, Benjamin Sach

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


We present space lower bounds for online pattern matching under a number of different distance measures. Given a pattern of length m and a text that arrives one character at a time, the online pattern matching problem is to report the distance between the pattern and a sliding window of the text as soon as the new character arrives. We require that the correct answer is given at each position with constant probability. We give Ω(m) bit space lower bounds for L 1, L 2, L , Hamming, edit and swap distances as well as for any algorithm that computes the cross-correlation/convolution. We then show a dichotomy between distance functions that have wildcard-like properties and those that do not. In the former case which includes, as an example, pattern matching with character classes, we give Ω(m) bit space lower bounds. For other distance functions, we show that there exist space bounds of Ω(logm) and O(log 2 m) bits. Finally we discuss space lower bounds for non-binary inputs and show how in some cases they can be improved.

Original languageEnglish
Title of host publicationCombinatorial Pattern Matching - 22nd Annual Symposium, CPM 2011, Proceedings
Number of pages13
StatePublished - 2011
Event22nd Annual Symposium on Combinatorial Pattern Matching, CPM 2011 - Palermo, Italy
Duration: 27 Jun 201129 Jun 2011

Publication series

NameLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume6661 LNCS


Conference22nd Annual Symposium on Combinatorial Pattern Matching, CPM 2011

All Science Journal Classification (ASJC) codes

  • Theoretical Computer Science
  • General Computer Science


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