### Abstract

We study which property testing and sublinear time algorithms can be transformed into graph streaming algorithms for random order streams. Our main result is that for bounded degree graphs, any property that is constant-query testable in the adjacency list model can be tested with constant space in a single-pass in random order streams. Our result is obtained by estimating the distribution of local neighborhoods of the vertices on a random order graph stream using constant space. We then show that our approach can also be applied to constant time approximation algorithms for bounded degree graphs in the adjacency list model: As an example, we obtain a constant-space single-pass random order streaming algorithms for approximating the size of a maximum matching with additive error ∈n (n is the number of nodes). Our result establishes for the first time that a large class of sublinear algorithms can be simulated in random order streams, while Ω (n) space is needed for many graph streaming problems for adversarial orders.

Original language | English (US) |
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Title of host publication | 44th International Colloquium on Automata, Languages, and Programming, ICALP 2017 |

Editors | Anca Muscholl, Piotr Indyk, Fabian Kuhn, Ioannis Chatzigiannakis |

Publisher | Schloss Dagstuhl- Leibniz-Zentrum fur Informatik GmbH, Dagstuhl Publishing |

ISBN (Electronic) | 9783959770415 |

DOIs | |

State | Published - Jul 1 2017 |

Event | 44th International Colloquium on Automata, Languages, and Programming, ICALP 2017 - Warsaw, Poland Duration: Jul 10 2017 → Jul 14 2017 |

### Publication series

Name | Leibniz International Proceedings in Informatics, LIPIcs |
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Volume | 80 |

ISSN (Print) | 1868-8969 |

### Conference

Conference | 44th International Colloquium on Automata, Languages, and Programming, ICALP 2017 |
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Country | Poland |

City | Warsaw |

Period | 7/10/17 → 7/14/17 |

### Fingerprint

### Keywords

- Constant-time approximation algorithms
- Graph property testing
- Graph streaming algorithms

### ASJC Scopus subject areas

- Software

### Cite this

*44th International Colloquium on Automata, Languages, and Programming, ICALP 2017*[131] (Leibniz International Proceedings in Informatics, LIPIcs; Vol. 80). Schloss Dagstuhl- Leibniz-Zentrum fur Informatik GmbH, Dagstuhl Publishing. https://doi.org/10.4230/LIPIcs.ICALP.2017.131

**Testable bounded degree graph properties are random order streamable.** / Monemizadeh, Morteza; Muthukrishnan, Shanmugavelayutham; Peng, Pan; Sohler, Christian.

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution

*44th International Colloquium on Automata, Languages, and Programming, ICALP 2017.*, 131, Leibniz International Proceedings in Informatics, LIPIcs, vol. 80, Schloss Dagstuhl- Leibniz-Zentrum fur Informatik GmbH, Dagstuhl Publishing, 44th International Colloquium on Automata, Languages, and Programming, ICALP 2017, Warsaw, Poland, 7/10/17. https://doi.org/10.4230/LIPIcs.ICALP.2017.131

}

TY - GEN

T1 - Testable bounded degree graph properties are random order streamable

AU - Monemizadeh, Morteza

AU - Muthukrishnan, Shanmugavelayutham

AU - Peng, Pan

AU - Sohler, Christian

PY - 2017/7/1

Y1 - 2017/7/1

N2 - We study which property testing and sublinear time algorithms can be transformed into graph streaming algorithms for random order streams. Our main result is that for bounded degree graphs, any property that is constant-query testable in the adjacency list model can be tested with constant space in a single-pass in random order streams. Our result is obtained by estimating the distribution of local neighborhoods of the vertices on a random order graph stream using constant space. We then show that our approach can also be applied to constant time approximation algorithms for bounded degree graphs in the adjacency list model: As an example, we obtain a constant-space single-pass random order streaming algorithms for approximating the size of a maximum matching with additive error ∈n (n is the number of nodes). Our result establishes for the first time that a large class of sublinear algorithms can be simulated in random order streams, while Ω (n) space is needed for many graph streaming problems for adversarial orders.

AB - We study which property testing and sublinear time algorithms can be transformed into graph streaming algorithms for random order streams. Our main result is that for bounded degree graphs, any property that is constant-query testable in the adjacency list model can be tested with constant space in a single-pass in random order streams. Our result is obtained by estimating the distribution of local neighborhoods of the vertices on a random order graph stream using constant space. We then show that our approach can also be applied to constant time approximation algorithms for bounded degree graphs in the adjacency list model: As an example, we obtain a constant-space single-pass random order streaming algorithms for approximating the size of a maximum matching with additive error ∈n (n is the number of nodes). Our result establishes for the first time that a large class of sublinear algorithms can be simulated in random order streams, while Ω (n) space is needed for many graph streaming problems for adversarial orders.

KW - Constant-time approximation algorithms

KW - Graph property testing

KW - Graph streaming algorithms

UR - http://www.scopus.com/inward/record.url?scp=85027275236&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=85027275236&partnerID=8YFLogxK

U2 - 10.4230/LIPIcs.ICALP.2017.131

DO - 10.4230/LIPIcs.ICALP.2017.131

M3 - Conference contribution

AN - SCOPUS:85027275236

T3 - Leibniz International Proceedings in Informatics, LIPIcs

BT - 44th International Colloquium on Automata, Languages, and Programming, ICALP 2017

A2 - Muscholl, Anca

A2 - Indyk, Piotr

A2 - Kuhn, Fabian

A2 - Chatzigiannakis, Ioannis

PB - Schloss Dagstuhl- Leibniz-Zentrum fur Informatik GmbH, Dagstuhl Publishing

ER -