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Communication cost of consensus for nodes with limited memory
Giulia Fanti1, Nina Holden2, Yuval Peres3
1Department of Electrical and Computer Engineering, Carnegie Mellon University, Pittsburgh, PA 15213.
Summary
Reaching consensus on the majority bit in wireless networks requires sufficient memory. Insufficient memory prevents nodes from knowing when to stop communicating, increasing communication costs.
Area of Science:
- Computer Science
- Electrical Engineering
- Network Science
Background:
- Wireless networks and the Internet of Things (IoT) require efficient consensus mechanisms.
- Existing research prioritizes consensus time and error probability, not communication cost.
Purpose of the Study:
- To minimize communication costs for reaching consensus on the majority bit among n nodes.
- To investigate the impact of node memory on communication efficiency.
Main Methods:
- Modeling nodes as finite automata with Poisson clocks.
- Analyzing consensus probability based on node memory (m bits).
- Determining conditions for linear communication cost.
Main Results:
- Consensus is achievable with linear communication cost when memory (m) is sufficient (m >= 2).
- Consensus with linear communication cost is impossible if memory is insufficient (m < 2).
- Nodes cannot reliably detect consensus completion with low memory, hindering communication reduction.
Conclusions:
- Sufficient node memory is crucial for efficient consensus in distributed systems.
- Memory limitations fundamentally restrict the ability to minimize communication in consensus protocols.
- Future research should consider memory constraints in designing consensus algorithms for IoT and wireless networks.
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