The Landscape of Compressibility Measures for Two-Dimensional Data Article Swipe
L. Carfagna
,
Giovanni Manzini
·
YOU?
·
· 2024
· Open Access
·
· DOI: https://doi.org/10.1109/access.2024.3417621
YOU?
·
· 2024
· Open Access
·
· DOI: https://doi.org/10.1109/access.2024.3417621
In this paper we extend to two-dimensional data two recently introduced one-dimensional compressibility measures: the measure defined in terms of the smallest string attractor, and the measure defined in terms of the number of distinct substrings of the input string. Concretely, we introduce the two-dimensional measures and , as natural generalizations of and , and we initiate the study of their properties. Among other things, we prove that is monotone and can be computed in linear time, and we show that, although it is still true that , the gap between the two measures can be and therefore asymptotically larger than the gap between and . To complete the scenario of two-dimensional compressibility measures, we introduce the measure which generalizes to two dimensions the notion of optimal parsing. We prove that, somewhat surprisingly, the relationship between and is significantly different than in the one-dimensional case. As an application of our results we provide the first analysis of the space usage of the two-dimensional block tree introduced in [Brisaboa et al., Two-dimensional block trees, The computer Journal, 2024]. Our analysis shows that the space usage can be bounded in terms of both and . Finally, using insights from our analysis, we design the first linear time and space algorithm for constructing the two-dimensional block tree for arbitrary matrices.
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- Type
- article
- Language
- en
- Landing Page
- http://doi.org/10.1109/access.2024.3417621
- OA Status
- gold
- Cited By
- 2
- References
- 25
- Related Works
- 10
- OpenAlex ID
- https://openalex.org/W4399881307
All OpenAlex metadata
Raw OpenAlex JSON
- OpenAlex ID
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https://openalex.org/W4399881307Canonical identifier for this work in OpenAlex
- DOI
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https://doi.org/10.1109/access.2024.3417621Digital Object Identifier
- Title
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The Landscape of Compressibility Measures for Two-Dimensional DataWork title
- Type
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articleOpenAlex work type
- Language
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enPrimary language
- Publication year
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2024Year of publication
- Publication date
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2024-01-01Full publication date if available
- Authors
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L. Carfagna, Giovanni ManziniList of authors in order
- Landing page
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https://doi.org/10.1109/access.2024.3417621Publisher landing page
- Open access
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YesWhether a free full text is available
- OA status
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goldOpen access status per OpenAlex
- OA URL
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https://doi.org/10.1109/access.2024.3417621Direct OA link when available
- Concepts
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Compressibility, Computer science, Physics, MechanicsTop concepts (fields/topics) attached by OpenAlex
- Cited by
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2Total citation count in OpenAlex
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2025: 1, 2024: 1Per-year citation counts (last 5 years)
- References (count)
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25Number of works referenced by this work
- Related works (count)
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10Other works algorithmically related by OpenAlex
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| abstract_inverted_index.two-dimensional | 6, 54, 165, 229, 287 |
| abstract_inverted_index.<inline-formula> | 15, 31, 56, 62, 71, 77, 96, 120, 135, 149, 155, 172, 194, 199, 258, 264 |
| abstract_inverted_index.Journal</italic>, | 242 |
| abstract_inverted_index.notation="LaTeX">$\Omega | 137 |
| abstract_inverted_index.notation="LaTeX">$\delta | 33, 64, 79, 98, 122, 157, 266 |
| abstract_inverted_index.notation="LaTeX">$\gamma | 17, 58, 73, 151, 201, 260 |
| abstract_inverted_index.notation="LaTeX">$b_{2D}$ | 174, 196 |
| abstract_inverted_index.</tex-math></inline-formula> | 19, 35, 60, 75, 100, 140, 153, 175, 197, 203, 262 |
| abstract_inverted_index.</tex-math></inline-formula>, | 66, 81, 126 |
| abstract_inverted_index.</tex-math></inline-formula>. | 159, 268 |
| cited_by_percentile_year.max | 95 |
| cited_by_percentile_year.min | 90 |
| countries_distinct_count | 1 |
| institutions_distinct_count | 2 |
| sustainable_development_goals[0].id | https://metadata.un.org/sdg/11 |
| sustainable_development_goals[0].score | 0.47999998927116394 |
| sustainable_development_goals[0].display_name | Sustainable cities and communities |
| sustainable_development_goals[1].id | https://metadata.un.org/sdg/13 |
| sustainable_development_goals[1].score | 0.4000000059604645 |
| sustainable_development_goals[1].display_name | Climate action |
| citation_normalized_percentile.value | 0.78382049 |
| citation_normalized_percentile.is_in_top_1_percent | False |
| citation_normalized_percentile.is_in_top_10_percent | False |