### Abstract

We give cell-probe bounds for the computation of edit distance, Hamming distance, convolution and longest common subsequence in a stream. In this model, a fixed string of $n$ symbols is given and one $\delta$-bit symbol arrives at a time in a stream. After each symbol arrives, the distance between the fixed string and a suffix of most recent symbols of the stream is reported. The cell-probe model is perhaps the strongest model of computation for showing data structure lower bounds, subsuming in particular the popular word-RAM model. * We first give an $\Omega((\delta \log n)/(w+\log\log n))$ lower bound for the time to give each output for both online Hamming distance and convolution, where $w$ is the word size. This bound relies on a new encoding scheme and for the first time holds even when $w$ is as small as a single bit. * We then consider the online edit distance and longest common subsequence problems in the bit-probe model ($w=1$) with a constant sized input alphabet. We give a lower bound of $\Omega(\sqrt{\log n}/(\log\log n)^{3/2})$ which applies for both problems. This second set of results relies both on our new encoding scheme as well as a carefully constructed hard distribution. * Finally, for the online edit distance problem we show that there is an $O((\log n)^2/w)$ upper bound in the cell-probe model. This bound gives a contrast to our new lower bound and also establishes an exponential gap between the known cell-probe and RAM model complexities.

Original language | English |
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Title of host publication | ACM-SIAM Symposium on Discrete Algorithms |

Publication status | Published - 4 Jan 2015 |

Event | ACM-SIAM Symposium on Discrete Algorithms (2015) - San Diego, United States Duration: 4 Jan 2015 → 6 Jan 2015 Conference number: 26 |

### Conference

Conference | ACM-SIAM Symposium on Discrete Algorithms (2015) |
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Abbreviated title | SODA15 |

Country | United States |

City | San Diego |

Period | 4/01/15 → 6/01/15 |

### Bibliographical note

Accepted: 9th September 2014### Keywords

- cs.DS
- F.2.2; F.1.2

## Fingerprint Dive into the research topics of 'Cell-Probe Bounds for Online Edit Distance and Other Pattern Matching Problems'. Together they form a unique fingerprint.

## Profiles

## Dr Raphael Clifford

- Department of Computer Science - Reader in Algorithm Design
- Intelligent Systems Laboratory
- Theory and Algorithms

Person: Academic , Member, Group lead

## Cite this

Clifford, R., Jalsenius, M., & Sach, B. (2015). Cell-Probe Bounds for Online Edit Distance and Other Pattern Matching Problems. In

*ACM-SIAM Symposium on Discrete Algorithms*