TY - GEN
T1 - Polynomial counting in anonymous dynamic networks with applications to anonymous dynamic algebraic computations
AU - Kowalski, Dariusz R.
AU - Mosteiro, Miguel A.
N1 - Funding Information:
Supported by Polish National Science Center grant UMO-2015/17/B/ST6/01897. 2 Research work partially supported by Pace University Scholarly Research Award P1258 and the UK Royal Society Grant IES\R3\170293.
Funding Information:
1 Supported by Polish National Science Center grant UMO-2015/17/B/ST6/01897. 2 Research work partially supported by Pace University Scholarly Research Award P1258 and the UK Royal Society Grant IES/R3/170293.
Publisher Copyright:
© 2018 Schloss Dagstuhl- Leibniz-Zentrum fur Informatik GmbH, Dagstuhl Publishing. All rights reserved.
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
T2 - 45th International Colloquium on Automata, Languages, and Programming, ICALP 2018
Y2 - 9 July 2018 through 13 July 2018
ER -