### Abstract

Starting with Michail, Chatzigiannakis, and Spirakis work [20], the problem of Counting the number of nodes in Anonymous Dynamic Networks has attracted a lot of attention. The problem is challenging because nodes are indistinguishable (they lack identifiers and execute the same program) and the topology may change arbitrarily from round to round of communication, as long as the network is connected in each round. The problem is central in distributed computing as the number of participants is frequently needed to make important decisions, such as termination, agreement, synchronization, and many others. A variety of algorithms built on top of mass-distribution techniques have been presented, analyzed, and also experimentally evaluated; some of them assumed additional knowledge of network characteristics, such as bounded degree or given upper bound on the network size. However, the question of whether Counting can be solved deterministically in sub-exponential time remained open. In this work, we answer this question positively by presenting Methodical Counting, which runs in polynomial time and requires no knowledge of network characteristics. Moreover, we also show how to extend Methodical Counting to compute the sum of input values and more complex functions without extra cost. Our analysis leverages previous work on random walks in evolving graphs, combined with carefully chosen alarms in the algorithm that control the process and its parameters. To the best of our knowledge, our Counting algorithm and its extensions to other algebraic and Boolean functions are the first that can be implemented in practice with worst-case guarantees.

Original language | English (US) |
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Title of host publication | 45th International Colloquium on Automata, Languages, and Programming, ICALP 2018 |

Editors | Christos Kaklamanis, Daniel Marx, Ioannis Chatzigiannakis, Donald Sannella |

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

ISBN (Electronic) | 9783959770767 |

DOIs | |

State | Published - Jul 1 2018 |

Event | 45th International Colloquium on Automata, Languages, and Programming, ICALP 2018 - Prague, Czech Republic Duration: Jul 9 2018 → Jul 13 2018 |

### Publication series

Name | Leibniz International Proceedings in Informatics, LIPIcs |
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Volume | 107 |

ISSN (Print) | 1868-8969 |

### Other

Other | 45th International Colloquium on Automata, Languages, and Programming, ICALP 2018 |
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Country | Czech Republic |

City | Prague |

Period | 7/9/18 → 7/13/18 |

### Fingerprint

### Keywords

- Anonymous dynamic networks
- Boolean functions
- Counting
- Deterministic algorithms
- Distributed algorithms

### ASJC Scopus subject areas

- Software

### Cite this

*45th International Colloquium on Automata, Languages, and Programming, ICALP 2018*[156] (Leibniz International Proceedings in Informatics, LIPIcs; Vol. 107). Schloss Dagstuhl- Leibniz-Zentrum fur Informatik GmbH, Dagstuhl Publishing. https://doi.org/10.4230/LIPIcs.ICALP.2018.156

**Polynomial counting in anonymous dynamic networks with applications to anonymous dynamic algebraic computations.** / Kowalski, Dariusz R.; Mosteiro, Miguel A.

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

*45th International Colloquium on Automata, Languages, and Programming, ICALP 2018.*, 156, Leibniz International Proceedings in Informatics, LIPIcs, vol. 107, Schloss Dagstuhl- Leibniz-Zentrum fur Informatik GmbH, Dagstuhl Publishing, 45th International Colloquium on Automata, Languages, and Programming, ICALP 2018, Prague, Czech Republic, 7/9/18. https://doi.org/10.4230/LIPIcs.ICALP.2018.156

}

TY - GEN

T1 - Polynomial counting in anonymous dynamic networks with applications to anonymous dynamic algebraic computations

AU - Kowalski, Dariusz R.

AU - Mosteiro, Miguel A.

PY - 2018/7/1

Y1 - 2018/7/1

N2 - Starting with Michail, Chatzigiannakis, and Spirakis work [20], the problem of Counting the number of nodes in Anonymous Dynamic Networks has attracted a lot of attention. The problem is challenging because nodes are indistinguishable (they lack identifiers and execute the same program) and the topology may change arbitrarily from round to round of communication, as long as the network is connected in each round. The problem is central in distributed computing as the number of participants is frequently needed to make important decisions, such as termination, agreement, synchronization, and many others. A variety of algorithms built on top of mass-distribution techniques have been presented, analyzed, and also experimentally evaluated; some of them assumed additional knowledge of network characteristics, such as bounded degree or given upper bound on the network size. However, the question of whether Counting can be solved deterministically in sub-exponential time remained open. In this work, we answer this question positively by presenting Methodical Counting, which runs in polynomial time and requires no knowledge of network characteristics. Moreover, we also show how to extend Methodical Counting to compute the sum of input values and more complex functions without extra cost. Our analysis leverages previous work on random walks in evolving graphs, combined with carefully chosen alarms in the algorithm that control the process and its parameters. To the best of our knowledge, our Counting algorithm and its extensions to other algebraic and Boolean functions are the first that can be implemented in practice with worst-case guarantees.

AB - Starting with Michail, Chatzigiannakis, and Spirakis work [20], the problem of Counting the number of nodes in Anonymous Dynamic Networks has attracted a lot of attention. The problem is challenging because nodes are indistinguishable (they lack identifiers and execute the same program) and the topology may change arbitrarily from round to round of communication, as long as the network is connected in each round. The problem is central in distributed computing as the number of participants is frequently needed to make important decisions, such as termination, agreement, synchronization, and many others. A variety of algorithms built on top of mass-distribution techniques have been presented, analyzed, and also experimentally evaluated; some of them assumed additional knowledge of network characteristics, such as bounded degree or given upper bound on the network size. However, the question of whether Counting can be solved deterministically in sub-exponential time remained open. In this work, we answer this question positively by presenting Methodical Counting, which runs in polynomial time and requires no knowledge of network characteristics. Moreover, we also show how to extend Methodical Counting to compute the sum of input values and more complex functions without extra cost. Our analysis leverages previous work on random walks in evolving graphs, combined with carefully chosen alarms in the algorithm that control the process and its parameters. To the best of our knowledge, our Counting algorithm and its extensions to other algebraic and Boolean functions are the first that can be implemented in practice with worst-case guarantees.

KW - Anonymous dynamic networks

KW - Boolean functions

KW - Counting

KW - Deterministic algorithms

KW - Distributed algorithms

UR - http://www.scopus.com/inward/record.url?scp=85049801273&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=85049801273&partnerID=8YFLogxK

U2 - 10.4230/LIPIcs.ICALP.2018.156

DO - 10.4230/LIPIcs.ICALP.2018.156

M3 - Conference contribution

AN - SCOPUS:85049801273

T3 - Leibniz International Proceedings in Informatics, LIPIcs

BT - 45th International Colloquium on Automata, Languages, and Programming, ICALP 2018

A2 - Kaklamanis, Christos

A2 - Marx, Daniel

A2 - Chatzigiannakis, Ioannis

A2 - Sannella, Donald

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

ER -