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The Cartographer
On the Size of Lempel-Ziv and Lyndon Factorizations
November 27, 2016 Β· Declared Dead Β· π Symposium on Theoretical Aspects of Computer Science
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Authors
Juha KΓ€rkkΓ€inen, Dominik Kempa, Yuto Nakashima, Simon J. Puglisi, Arseny M. Shur
arXiv ID
1611.08898
Category
cs.DS: Data Structures & Algorithms
Cross-listed
cs.DM
Citations
18
Venue
Symposium on Theoretical Aspects of Computer Science
Last Checked
3 months ago
Abstract
Lyndon factorization and Lempel-Ziv (LZ) factorization are both important tools for analysing the structure and complexity of strings, but their combinatorial structure is very different. In this paper, we establish the first direct connection between the two by showing that while the Lyndon factorization can be bigger than the non-overlapping LZ factorization (which we demonstrate by describing a new, non-trivial family of strings) it is never more than twice the size.
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