A One Pass Streaming Algorithm for Finding Euler Tours Article Swipe
Christian Glazik
,
Jan Schiemann
,
Anand Srivastav
·
YOU?
·
· 2022
· Open Access
·
· DOI: https://doi.org/10.1007/s00224-022-10077-w
YOU?
·
· 2022
· Open Access
·
· DOI: https://doi.org/10.1007/s00224-022-10077-w
Given an undirected graph G on n nodes and m edges in the form of a data stream we study the problem of finding an Euler tour in G . Our main result is the first one-pass streaming algorithm computing an Euler tour of G in the form of an edge successor function with only $\mathcal O(n\log (n))$ RAM, which is optimal for this setting (e.g. Sun and Woodruff (2015)). Since the output size can be much larger, we use a write-only tape to gradually output the solution. The previously best-known result for finding Euler tours in data streams is implicitly given by the W-stream algorithm of Demetrescu et al. (2010) using $\mathcal O(m/n)$ passes under the same RAM limitation. Our approach is to partition the edges into edge-disjoint cycles and to merge the cycles until a single Euler tour is achieved. In the streaming environment such a merging is far from being obvious as the limited RAM allows the processing of only a constant number of cycles at once. This enforces merging of cycles that partially are no longer present in RAM. We solve this problem with a new edge swapping technique, for which storing two certain edges per node is sufficient to merge tours without having all tour edges in RAM. The mathematical key is to model tours and their merging in an algebraic way, where certain equivalence classes represent subtours. This quite general approach might be of interest also in other routing problems.
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- Type
- article
- Language
- en
- Landing Page
- https://doi.org/10.1007/s00224-022-10077-w
- https://link.springer.com/content/pdf/10.1007/s00224-022-10077-w.pdf
- OA Status
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- References
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- OpenAlex ID
- https://openalex.org/W4312131249
All OpenAlex metadata
Raw OpenAlex JSON
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https://openalex.org/W4312131249Canonical identifier for this work in OpenAlex
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https://doi.org/10.1007/s00224-022-10077-wDigital Object Identifier
- Title
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A One Pass Streaming Algorithm for Finding Euler ToursWork title
- Type
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articleOpenAlex work type
- Language
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enPrimary language
- Publication year
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2022Year of publication
- Publication date
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2022-12-12Full publication date if available
- Authors
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Christian Glazik, Jan Schiemann, Anand SrivastavList of authors in order
- Landing page
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https://doi.org/10.1007/s00224-022-10077-wPublisher landing page
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https://link.springer.com/content/pdf/10.1007/s00224-022-10077-w.pdfDirect link to full text PDF
- Open access
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YesWhether a free full text is available
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hybridOpen access status per OpenAlex
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https://link.springer.com/content/pdf/10.1007/s00224-022-10077-w.pdfDirect OA link when available
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Algorithm, Computer science, Artificial intelligenceTop concepts (fields/topics) attached by OpenAlex
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2Total citation count in OpenAlex
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2022: 2Per-year citation counts (last 5 years)
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10Other works algorithmically related by OpenAlex
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| abstract_inverted_index.$\mathcal | 56, 115 |
| abstract_inverted_index.<mml:math | 59, 117 |
| abstract_inverted_index.achieved. | 146 |
| abstract_inverted_index.algebraic | 230 |
| abstract_inverted_index.algorithm | 39, 108 |
| abstract_inverted_index.computing | 40 |
| abstract_inverted_index.gradually | 87 |
| abstract_inverted_index.partially | 181 |
| abstract_inverted_index.partition | 129 |
| abstract_inverted_index.problems. | 250 |
| abstract_inverted_index.represent | 236 |
| abstract_inverted_index.solution. | 90 |
| abstract_inverted_index.streaming | 38, 149 |
| abstract_inverted_index.subtours. | 237 |
| abstract_inverted_index.successor | 52 |
| abstract_inverted_index.Demetrescu | 110 |
| abstract_inverted_index.best-known | 93 |
| abstract_inverted_index.implicitly | 103 |
| abstract_inverted_index.previously | 92 |
| abstract_inverted_index.processing | 165 |
| abstract_inverted_index.sufficient | 207 |
| abstract_inverted_index.technique, | 197 |
| abstract_inverted_index.undirected | 3 |
| abstract_inverted_index.write-only | 84 |
| abstract_inverted_index.environment | 150 |
| abstract_inverted_index.equivalence | 234 |
| abstract_inverted_index.limitation. | 124 |
| abstract_inverted_index.mathematical | 219 |
| abstract_inverted_index.edge-disjoint | 133 |
| abstract_inverted_index.xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mi>O</mml:mi><mml:mo>(</mml:mo><mml:mi>m</mml:mi><mml:mo>/</mml:mo><mml:mi>n</mml:mi><mml:mo>)</mml:mo></mml:math> | 118 |
| abstract_inverted_index.xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mi>O</mml:mi><mml:mo>(</mml:mo><mml:mi>n</mml:mi><mml:mi>log</mml:mi><mml:mo>(</mml:mo><mml:mi>n</mml:mi><mml:mo>)</mml:mo><mml:mo>)</mml:mo></mml:math> | 60 |
| cited_by_percentile_year.max | 96 |
| cited_by_percentile_year.min | 94 |
| corresponding_author_ids | https://openalex.org/A5012713429 |
| countries_distinct_count | 1 |
| institutions_distinct_count | 3 |
| corresponding_institution_ids | https://openalex.org/I32021983 |
| citation_normalized_percentile.value | 0.62660644 |
| citation_normalized_percentile.is_in_top_1_percent | False |
| citation_normalized_percentile.is_in_top_10_percent | False |