# Communication cost of consensus for nodes with limited memory

@article{Fanti2019CommunicationCO, title={Communication cost of consensus for nodes with limited memory}, author={Giulia C. Fanti and Nina Holden and Yuval Peres and Gireeja Ranade}, journal={Proceedings of the National Academy of Sciences}, year={2019}, volume={117}, pages={5624 - 5630} }

Significance Algorithms that allow a large number, n, of processors to reach consensus are of substantial current interest due to applications in sensor networks and blockchains. When each processor is assigned an initial bit, the consensus bit should match the majority of these bits with high probability. We present a consensus algorithm where the total number of communications between all processors grows linearly in n, yet each processor uses surprisingly few bits of memory; we also prove a…

## 9 Citations

### On fast probabilistic consensus in the Byzantine setting

- Computer Science, MathematicsArXiv
- 2019

A leaderless protocol of low communicational complexity which allows a set of nodes to come to a consensus on a value of a bit and makes use of a sequence of random numbers which are either provided by a trusted source or generated by the nodes themselves using some decentralized random number generating protocol.

### Consensus with Bounded Space and Minimal Communication

- Computer ScienceArXiv
- 2021

A protocol is designed that shows the lower bound is sharp, solving an open problem from [FHPR20], the population protocol model focusing on the communication complexity needed to achieve consensus with high probability.

### FPC-BI: Fast Probabilistic Consensus within Byzantine Infrastructures

- Computer Science, MathematicsJ. Parallel Distributed Comput.
- 2021

### Voting-based probabilistic consensuses and their applications in distributed ledgers

- Computer Science, MathematicsAnnals of Telecommunications
- 2021

The Fast Probabilistic Consensus (FPC) protocol is discussed, which circumvents the problems mentioned above by using external randomness.

### Voting-based probabilistic consensuses and their applications in distributed ledgers

- Mathematics, Computer ScienceAnn. des Télécommunications
- 2022

The Fast Probabilistic Consensus (FPC) protocol is discussed, which circumvents the problems mentioned above by using external randomness.

### The Problem of Distributed Consensus: A Survey

- Computer Science, MathematicsArXiv
- 2021

A survey is given of approaches to the problem of distributed consensus, focusing particularly on methods based on cellular automata and related systems, as well as a history of the field and an extensive bibliography.

### ppsim: A software package for efficiently simulating and visualizing population protocols

- Computer ScienceCMSB
- 2021

We introduce ppsim [2], a software package for efficiently simulating population protocols, a widely-studied subclass of chemical reaction networks (CRNs) in which all reactions have two reactants…

### MB-PBA: Leveraging Merkle Tree and Blockchain to Enhance User Profile-based Authentication in E-Learning Systems

- Computer Science2019 19th International Symposium on Communications and Information Technologies (ISCIT)
- 2019

The dominant features of the Merkle tree data structure and smart contracts on Blockchain are utilized to improve the User profile-based authentication approach and simplifies identity authentication, protects user confidential information, and enhances the security factor in terms of data integrity, user information transparency, and system availability.

### The Coordicide

- Physics
- 2020

4 Autopeering 17 4.1 Peer discovery . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17 4.2 Neighbor selection . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18 4.3 Network…

## 46 References

### A Polylogarithmic Gossip Algorithm for Plurality Consensus

- Computer SciencePODC
- 2016

An algorithm is presented that with high probability reaches plurality consensus in O(log k log n) rounds, while having message and memory size of log k + O (1) bits.

### An upper bound on the convergence time for quantized consensus

- Computer ScienceINFOCOM
- 2013

The theory of electric networks, random walks, and couplings of Markov chains are used to derive an upper bound for the expected convergence time on an arbitrary graph of size N, improving on the state of art bound of O(N4 log N) for binary consensus and O( N5) for quantized consensus algorithms.

### Using Three States for Binary Consensus on Complete Graphs

- Computer ScienceIEEE INFOCOM 2009
- 2009

It is shown that extending both the signaling and memory by just one state dramatically improves the reliability and speed of reaching the correct consensus and is therefore faster than purely binary systems.

### Convergence Speed of Binary Interval Consensus

- Computer Science2010 Proceedings IEEE INFOCOM
- 2010

An upper bound on the expected convergence time that holds for arbitrary connected graphs, which is based on the location of eigenvalues of some contact rate matrices is derived, and insights are provided on how the expected converge time depends on the network topology.

### Space-Optimal Majority in Population Protocols

- Computer ScienceSODA
- 2018

A new lower bound of $\Omega(\log n)$ states is provided for any protocol which stabilizes in n^{1-c} ) time, for any $c > 0$ constant, conditional on basic monotonicity and output assumptions, satisfied by all known protocols.

### Fast and Exact Majority in Population Protocols

- Computer SciencePODC
- 2015

This paper presents a new protocol called Average and Conquer (AVC), which shows that the majority problem can be solved exactly in time poly-logarithmic in n, provided that the memory per node is s = s = 1/ε + log n log{1/ε).

### Polylogarithmic-Time Leader Election in Population Protocols

- Computer ScienceICALP
- 2015

The argument combines careful use of concentration inequalities with anti-concentration bounds, showing that the leaders' values become spread apart as the execution progresses, which in turn implies that straggling leaders get quickly eliminated.

### Population Protocols Are Fast

- Computer Science
- 2018

For the first time, it is shown that solutions to all of the fundamental tasks in distributed computing can be obtained using finite-state protocols, including leader election, aggregate and threshold functions on the population, such as majority computation, and plurality consensus.

### Time-Space Trade-offs in Population Protocols

- Computer ScienceSODA
- 2017

A unified lower bound is proved, which relates the space available per node with the time complexity achievable by a protocol, and the first result to characterize time complexity for protocols which employ super-constant number of states per node, and it is proved that fast, poly-logarithmic running times require protocols to have relatively large space costs.

### Computation in networks of passively mobile finite-state sensors

- Computer SciencePODC '04
- 2004

The computational power of networks of small resource-limited mobile agents is explored. Two new models of computation based on pairwise interactions of finite-state agents in populations of finite…